Why is it impossible for the reactor of the nuclear power plant to turn into an explosive nuclear bomb? Is it true that both work on the same principle of operation: the interactive fission chain reaction 235U/239Pu and the bombardment of uranium-235 by fast neutrons produce a fission chain reaction accompanied by an enormous thermal energy in addition to beta and gamma radiation?
The most probable fission products are known to be 94Sr amu and 140Xe amu plus two fast neutrons. If both reactions are a chain reaction and almost instantaneous, then why not?
 A: To expand upon John Darby's excellent answer with regards to Chernobyl specifically, where actually, to answer the original question, there is a school of thought that it might have done!
John writes:

The explosions at Chernobyl were a steam explosion, and a chemical
explosion caused by oxygen reacting with aerosolized graphite.

It is my understanding that there is some degree of scientific debate still ongoing about this, which is relevant to your original question. I am going to put forward another hypothesis on the origin of the first explosion mentioned here. It is not mine – and nor am I wedded to it – and there is a chance that it has subsequently been disproved. That being said…
These two explosions were witnessed by several eyewitnesses -- both at the plant and fishermen elsewhere. These explosions were both large, and the second, and largest, occurred a couple of seconds after the first. The first one is widely believed to have been a steam or vapor explosion where the energy in the hot cooling water together with the energy generated across the reactor core pressurized the steam pretty much instantaneously and to such a degree that it catastrophically failed while under load. Some authors estimate that the power of the RBMK reactor went up a factor at least 100 over its design value of 3.2 GW (thermal) for a few seconds. The next explosion is often described as a hydrogen explosion, where water present is hydrolysed by the extreme temperatures and pressures present by the zirconium fuel rod cladding, producing hydrogen and oxygen (which then subsequently exploded, and set the graphite moderator on fire).
However, some authors have posited a "nuclear jet" hypothesis that corresponds to this initial explosion being a prompt criticality event proper, and the second explosion being a chemical one. The main evidence for this hypothesis, first posited in 2009, comes from the geographical location of two radioisotopes of xenon, $^{133}$Xe and $^{133m}$Xe, which were experimentally detected at Cherepovets (a Russian city 370 km north of Moscow and 1000 km north-northeast of Chernobyl) about four days after the explosion. These xenon isotopes have a half life of 5.24 days and 2.19 days respectively; in "ordinary" reactor fission their ratio can be estimated through Monte-Carlo simulations, in which the fission process is modeled computationally. It's worth noting that these types of simulations are very well regarded; in my professional work (as a medical physicist) there are two packages that are largely used, MCNP4 (which requires an export license from the US government, claims to have a million man-hours of programming behind it, and, I believe, handles fission excellently) and Geant4 (which, being written by CERN and released to the world as open-source software, doesn't).
The three authors of this paper, from the Swedish Defence Research Agency, Meteorological and Hydrological Institute and Stockholm University, have done this accurately for the RMBK reactor type used in Chernobyl and have estimated a branching ratio for these two isotopes under differing power levels and thus what might be expected to be present within the reactor. The authors furthermore claim that the code used to produce this estimate is experimentally validated. Below are the expected branching ratios for thermal neutron fission in the reactor:

The authors then have the ability to try different scenarios in the distribution of the reactor core, and look at the production of $^{133}$Xe (or $^{133m}$Xe). One of the scenarios they examined is that one reactor rod had a prompt criticality incident and produced a nuclear explosion with an energy release equivalent to 75 tons of TNT. The reactor is destroyed in this process, and the ratios of the two isotopes then decay back towards equilibrium:
.
Now, the interesting thing about this is that the ratio experimentally detected in Cherepovets happens to line up almost exactly with this scenario, and it is claimed that it is not possible to easily explain it any other way, given the known time delay between explosion and detection, and the unambiguous determination of the isotopes (via gamma-ray spectroscopy):

The authors of this work also claim that another significant piece of experimental evidence comes from the curious fact that Cherepovets is far to the north/northeast of Chernobyl, yet the majority of the fallout and dispersed isotopes was observed went to the west and northwest, causing (famously) "radioactive sheep" in Wales, amongst other issues en route over Scandinavia. We have got a lot better at weather forecasting since the late 1980s, and again the authors of this work use historical observational data and modern models to simulate what may have occurred. They claim that a these simulations show, as a function height, that  a significant fraction of the large amount of liberated radioactive fission products at low altitudes would head northwest toward Scandinavia but, at higher altitudes made a sharp turn back east around the Gulfs of Riga and Finland. This would permit them to explain the geographical distribution of $^{133}$Xe/$^{133m}$Xe that matches with the measurement made in Cherepovets, by having a jet of nuclear material reaching about a 3 km altitude:

Finally, the authors make the (to me, far less proved) claims that this hypothesis explains the observations made by eye of the two explosions:

[...] a witness that was out fishing on the cooling pond some 500 m away
from Block 4 when the accident happened. He heard a large clap
followed by an explosion. Then, in a couple of seconds he saw a bright
blue flash that was followed by an enormous explosion. It is well
known that criticality accidents emit a blue flash, or rather glow,
which derives from fluorescence of excited oxygen and nitrogen atoms
in the air [and perhaps Cerenkov radiation].
[...]
[After the second explosion ] with the fuel fully exposed, the
air was irradiated, and the typical blue glow was lit. An
employee of the power plant, Alexander Yuvchenko,
has described how he and a colleague “ran out of the
building and saw half of the building gone and
the reactor emitting a blue glow of ionized air.” But,
the flash observed by the fishing man was a bright blue
flash before he heard the second explosion [and before reactor products were directly exposed to the air].

The authors make the argument that this blue flash has to be nuclear, unlike a blue glow, which may be thermal:

[As a steam] explosion would not create a flash, an explanation could be that
the surface of the jet peeled off some hot material to the air and/or
that the jet with a temperature of several tens of thousand degrees
heated a column of air around its track. Within a few seconds that hot
material would cool down through the temperature interval around
7000°K, where for a short time before it cooled down further, it would radiate blue light by blackbody radiation—a blue flash, not a glow

So, there you have it. One (admittedly small) potential for an (admittedly small) nuclear explosion in the worst nuclear disaster in human history.
Maybe.
A: To get the exponential nuclear chain reaction to occur such as that in a nuclear bomb, you have to reach critical mass in order to have the chain reaction occur. However, the "explosion" part wants to disperse the mass which reduces the mass below critical and ends the chain reaction.
So in order for an atomic weapon to work it needs to either initiate the chain reaction fast enough so the mass can't disperse in time or it needs to keep the mass together long enough for enough of the chain reaction to occur, and neither happens at random.
Otherwise the self-sustaining reaction just gets really hot and stays that way which is what happens in a meltdown.
A: A nuclear reactor cannot explode like a nuclear weapon.
For a thermal reactor -like Chernobyl or Three Mile Island- the neutron generation lifetime is too long.
For a fast reactor (and a thermal reactor) there is no mechanism for creating and maintaining a super prompt critical assembly sufficiently long for significant release of energy from fission.
You have to really work hard to assemble the correct material to create a nuclear weapon; you need to create a system that is super prompt critical using fast neutrons and remains so sufficiently long for the chain reaction to produce enough energy before pressure causes dis-assembly into a non-critical configuration. By super prompt critical is meant super critical on the prompt neutrons alone without having to wait for the delayed neutrons to contribute. See the Los Alamos Primer by Serber, available from Amazon: the early notes on the physics of a fission weapon from Los Alamos at the beginning of the Manhattan project.
The explosions at Chernobyl were a steam explosion, and a chemical explosion caused by oxygen reacting with aerosolized graphite. (At Three Mile Island the explosion was from oxygen reacting with hydrogen released from oxidation of the over-heated zircalloy fuel cladding.)
For a nuclear reactor, the safety concern is the removal of decay heat from the radioactive decay of fission products after the fission process is terminated. Decay heat is about 5% of full power at shutdown.
A major problem with the Chernobyl design is the core was over-moderated. Specifically, the graphite was the moderator and the cooling water was not needed as a moderator and in fact acted as a neutron poison. So when the cooling water was lost the reactor power increased: positive feedback. The old N reactor in the US was a graphite moderated, water cooled reactor used to produce Pu for the weapons program, but was specifically designed to not have this problem.
Also, Chernobyl did not have a robust reactor containment system, it had a reactor confinement system.
A: In brief,  the lack of a containment structure surrounding any nuclear fission chain reaction will lead to the core (nuclear material) either breaking up or quickly decaying sufficiently that the chain reaction is unsustainable.
Nuclear bombs use a strong container and (usually) a lot of high explosive to force the core to stay dense until the chain reaction reaches extremely high fission rates.  At that point the explosion still blows the core apart but the total energy released is "big" .
If I recall correctly, the Hiroshima and Nagasaki bombs' cores only fissioned about 5% of the nuclear matter.
A: There are three major issues at play.
Fast neutrons vs. thermal neutrons
When fission occurs, between 2 and 3 neutrons are emitted.  These are fast neutrons, that is they have a very high neutron energy, or kinetic energy.   In a reactor, they are slowed down by a moderator to become a "thermal neutron".
In a reactor, the name of the game is sustainable fission - that is, each fission causes 1.0 additional fissions.  (or maybe 1.02 if you're trying to increase power.)  At 1.0 this is called "criticality". Exceeding 1.0 is "supercritical" (above critical). But reactors aren't designed to exceed criticality by a whole lot, why give it the ability to something it should never, never do?
For the fuel typically used in a reactor, fast neutrons perform poorly. They are much less likely to cause another fission than a thermal neutron. Even a small reduction in performance breaks the ability to maintain criticality.  If fast neutrons were allowed to run amok in a reactor, it would just shut down.
And moderation takes time.  That will be important.
Prompt criticality vs delayed criticality
Look closely at the periodic table.  Notice that as atoms get bigger, they have proportionately more neutrons per proton.

*

*Oxygen-16 has 8 neutrons 8 protons, ratio 1.0.

*Iron-56 has 30 neutrons 26 protons, ratio 1.15.

*Iodine-127 has 74 neutrons and 53 protons, ratio 1.39.

*Tungsten-184 has 110 neutrons and 74 protons, ratio 1.48.

*Uranium-235 has 143 neutrons and 92 protons, ratio 1.55.

When Uranium-235 fissions, it expels 0-3 neutrons and splits into two new atoms with (between them) 140-143 neutrons and 92 protons.  That's still a ratio of 1.52-1.55 -- much too high a ratio for the smaller atoms they become.
For instance a common fission product is Iodine-135. 82 neutrons 53 protons (ratio 1.54, as expected) and that's way off for iodine. 8 neutrons too many!
This will cause the new atoms to "decay" via various decay modes. One decay mode is "neutron emission" - plain and simple they "throw" an excess neutron or two.  The time it takes is called the "half life".  (here we are back at "time" again).
These delayed neutrons are part of the neutron economy of the reactor, and the reactor is designed to rely on them.  This slows down the reactivity of the reactor to within human reaction times. For a reactor to sustain criticality entirely on "prompt (immediately generated) neutrons" would be bad, and make the reactor extremely uncontrollable.
I mentioned Iodine-135. That decays (via beta; a neutron becomes a proton) into Xenon-135, which loves to "eat" neutrons. (turning into harmless Xenon-136).  Normally this is just accounted for in the reactor's "neutron economy", but if you make a power reduction and hold it for 8-16 hours, the I-135 previously made by the full-power operation will become Xe-135 while the reactor is at reduced power. This disproportionate amount of Xe-135 will "poison the reactor" in what's called a "Xenon pit" or "Iodine pit".
Xenon decays on its own after 24 hours or so (into harmful Cs-135). But if you can't wait, some reactors include extra control rods that can be pulled out to increase reactivity enough to get critical and use neutrons to burn up the Xe-135.  Obviously, this is risky.  It's a great deal more risky if your reactor has a bizarre control rod design that increases reactivity when control rods start to be inserted, and then, you insert all of them at once. (And that is how an RBMK reactor explodes).
Holding the package together, though.
Prompt criticality is easy enough - just push enough fissile material together and it will just happen. It will generate an exponentially increasing amount of power until... that energy pushes the material apart, and you no longer have a critical mass. This brings an end to the criticality.
And that is what happened at Chornobyl - the power excursion caused a steam explosion that blew the reactor to pieces, making it unable to be critical anymore.
That's the rub with making a bomb - you want the bomb to do more than just crack the critical mass in two and quit, like it does in criticality accidents.   OK, so you build the bomb to be highly prompt supercritical, so all the fuel fissions in a microsecond (before the mass can physically disassemble itself).  The time unit they use is called the "shake". (of a lamb's tail).
And even if you figure out all that, there's another problem. To get to "highly prompt supercritical", you must pass through "barely critical".  And you're moving "at the speed of stuff", so it takes a whole lot of shakes. And probably a burger and fries.   If fission starts before full assembly, the nuclear energy developed will oppose the assembly energy and win, causing Rapid Unscheduled Disassembly before assembly can finish. So nuclear yield will be extremely poor.

A fizzle of something intended to be a bomb. It's hard to do better by accident.
All that to say, making a bomb work is super, super hard even when you're really trying.  Not something that is going to happen by accident, especially not on a machine that is engineered to be unable to do that.
A: A fission warhead uses implosion compression equally on all sides to achieve criticality. Whereas a reactor fissions in a controlled continuation. A bomb fissions virtually everything simultaneously.
An analogy is comparing a car's engine running to a fuel tank explosion.
So no. You'd have to squish all the fuel into a ball... surround it with explosives and have it all detonate simultaneously.
A: The nuclear explosive bomb and the nuclear reactor operate on the same operating principle: chain reaction of the interactive fission U 235. The bombardment of uranium 235 by fast neutrons produces a fission by chain reaction accompanied by an enormous thermal energy in addition to beta and gamma radiation.
The most likely fission products are Sr 94 amu and Xe 140 amu plus two fast neutrons. The reaction is therefore a chain reaction and almost instantaneous. The annihilation of mass in this reaction is 0.215 amu transformed into 200 Mev of energy according to Einstein's formula E = dm.c ^ 2. One kilogram of U 235 can produce approximately 7.2 x 10 ^ 13 joules "1.72 x 10 ^ 13 calories", which is equivalent to the heat produced by the combustion of 1800 tons of coal or Mazot. This is the main advantage of nuclear power plants.
1-The speed of the reaction is what distinguishes the explosive reaction of atomic bombs from the normal combustion reaction of nuclear reactors. For an explosion to occur, the reaction rate or the release of thermal energy must occur very quickly causing a very large pressure difference upstream and downstream of the resulting shock wave, otherwise no explosion will occur.
2-The objective of the nuclear bomb is to release an energy of about 8 x 10 ^ 13 joules, equivalent to 20,000 tons of highly explosive TNT, in about 20 seconds, while the power capacity of the reactor of the nuclear power plant can release the thermal from zero (emergency stop) to full station power, say 1000 MW (10 ^ 9 Joules per second).
3-The reaction rate in nuclear reactors is kept at a low level by using natural uranium composed of 0.74% U 235, 0.006% U 234 and 0.993 U 238 or enriching uranium 235 at a concentration limited to 3-5%. In addition, the U fuel is distributed over THOUSANDS of fuel rods over the entire large volume of the reactor core which is the opposite geometry of the nuclear bomb. The rest of the reactor core is mainly inert U 238, mixed with graphite or any other suitable moderator, which absorbs most of the neutrons from the reaction causing the transformation of U 238 to Pu 239.
*It should also be mentioned that Pu 239 is much more expensive than natural uranium where here we have a unique case where the price of fuel is absolutely negative. The reactor also uses movable Cd or boron alloy control rods for penetrate vertically into the core and absorb any desired amount of neutrons.

*

*In order to increase safety, the reactor core is contained inside a thick steel vessel surrounded by a concrete container reinforced with steel rods 1 to 2 meters thick, in the shape of a 'hemisphere.
-Conversely, in modern atomic bombs, the reaction is reinforced by a concentration of U-235 or Pu 239 enriched or fertilized to more than 90% with a mass of about 20-30 Kg, contained in the correct geometry, at inside a relatively small container equipped with explosive sources emitting fast neutrons. In addition, the material and design of the walls reflect the neutrons that escape inside the reaction.
** Even in the event of accidents or occurrences such as the shutdown of the control rods, an earthquake hitting the reactor, a series of cooling water pump failures, all causing excessive heating, the nuclear reactor CORE of a nuclear power plant can crack, break down, melt, but never explodes.

*This is why the Chernobyl reactor did not explode and cannot become like a nuclear bomb. It's really impossible, but it just melted and collapsed due to the overheating and swelling of its core.

