Nuclear Fusion requirements? So I kept searching for answers or reasons as to why the sun can generate nuclear fusion at 15 million degrees C when I research that nuclear fusion is achieved at 100 million degrees.
Is it because the conditions of conducting nuclear fusion differ from one another?
 A: Fusion can, in theory, occur at any temperature - even room temperature! It's just that the probability in that case is exponentially tiny (as in like mystically small meaning $10^{1000}$ or greater odds against; the kind of numbers that the ancients used to speculate about in wonder and awe, and not realistic numbers of things actually observable.).
The reason for this is that the atomic nucleus is fundamentally a balance between two forces: one is the electrostatic force that results from having a bunch of positive charges (the protons) hanging out next to each other and this wants to try and blow the thing apart, the other is the residual strong force, which is much shorter range (meaning it falls off much quicker with increasing separation) but typically much stronger, and wants to try and hold it together. On top of this balance is the weak force, which maintains a degree of balance in the ratio of the numbers of protons and neutrons by converting some to the other when they are not balanced (beta-plus and beta-minus decays). This last force is much weaker than the other two.
To get fusion, what you need, then, is to bring the nuclei involved close enough that the residual strong force exceeds the electrostatic force trying to push them apart. And this requires either doing a lot of work against the electrostatic force, or quantum tunneling - in particular, each nucleus has a wave function for its position just as electrons hanging out around a nucleus in an atom do so their positions are not fully well-defined, and that wave function extends, even at separation, into the region where the two nuclei are close enough to fuse, which means there is a probability to actually have had fusion by the time of the next "measurement". (The same is how radioactive decay works, roughly - the wave function of some nuclear particles extends outside the nucleus enough that you can detect a particle leaving with some probability. and thus you can pick them up with a measurer like Geiger counter.)
Now as you get them closer together, you can get the wave functions to hit regions of higher amplitude and so greater probability more often and thus a better chance at fusion. The trouble is, of course, you're working against that electrostatic repulsion and thus to get them to come close enough reliably, you need a lot of force to drive them together, but because of the tunneling effect, not as much as you'd need were these purely Newtonian particles.
And how do you generate more force? There's two ways: one is to increase the temperature, making them move around faster and so come closer by virtue of their kinetic energy, and another is to increase the pressure, mechanically pushing them closer together by increasing the density. In a fusion reactor, pressures are very low - almost vacuum, and so as a result, pretty much the only thing you have to work with is temperature, and thus it must be very high, e.g. 100 MK or more (that's megakelvins, or millions of kelvins, here. equiv to degrees C since the Kelvin/Celsius offset is negligible). The Sun, however, as you noticed, has a lower temperature of 15 MK at its core. The reason it's able to work, then, is because it has a lot more pressure - over 30 PPa - that's about 300 billion times the pressure of Earth's atmosphere, and 100 million times the pressure at the deepest parts of Earth's ocean (the Marianas Trench). If you had that kind of pressure in a nuclear fusion reactor at 100 MK+ temperature, it would become an H-bomb - and that is precisely why (in addition to the temperature) you need a fission bomb to build an H-bomb: it will not only heat the fuel to the requisite temperature but compress it dramatically.
A further factor to point out is the Sun's core and a fusion reactor or H-bomb are not quite the same thing in terms of the reaction they use: a man-made reactor and bomb uses deuterium fusion or deuterium-tritium (DT) fusion, while the Sun uses the proton-proton (PP) cycle which is fueled by common hydrogen, i.e. one proton only in the nucleus, versus the less-common deuterium, i.e. one proton and one neutron. Fusing two protons is very difficult because one proton with another is not stable (high repulsion), but a proton and a neutron is, and the only way proton-proton fusion can happen is if the weak force interaction is triggered at the same time to end up with deuterium by converting one to a neutron (beta-minus decay coincident with fusion), and the probability for both that AND the required tunneling is very small indeed. So even at the Sun's potent fusion conditions, actually fusion rates are very low compared even to those in a man-made reactor, and far, far lower than in a bomb. (Bomb-like fusion rates can occur in nature - but it's not with hydrogen stars, but rather carbon-oxygen (or similar) white dwarfs who accrete material from a stellar companion until they are compressed below their Chandrasekhar limit and begin collapse. When this happens the carbon and oxygen fuse at bomb levels and the whole thing detonates just as a bomb does only with tremendously more energy owing to incalculably more fuel (although C-O fuel is less energetic than hydrogen and/or deuterium/deuterium-tritium fuel) being present. Such an explosion is called a Type Ia supernova - and they have a fairly uniform brightness, which permits their use as so-called "standard candles" to find the distance to remote objects like galaxies in the deep cosmos, and thus are crucial for our cosmological studies.)
A: What you've just stumbled upon is the same puzzle that stumped many astrophysicists in the early 20th century. The "100 million degrees" figure you quote is indeed the temperature at which a significant portion of the plasma can undergo fusion reactions by overcoming the classical Coulomb barrier. But we know the Sun's core fuses hydrogen, so why is it colder than it should be? The answer has to do with density and quantum tunneling.
It turns out that confining plasma heated to millions of degrees is quite difficult. As such, in terrestrial fusion devices, we can only confine a small amount of low-density plasma at once, and so, in order to do anything meaningful, we have to heat it until most of it is fusing.
The Sun, however, has no trouble confining plasma; it does so effortlessly, with gravity. As such, it doesn't particularly care if most of the plasma is fusing, because there's no shortage of it, after all, and what's there is at very high density. In order to keep itself burning, only a small portion of the plasma needs to be at the right energy for fusion. Since, at any temperature, you'll always have a high-energy tail to your probability distribution for particle kinetic energies, it stands to reason that, even at a cooler temperature, there might be enough plasma fusing to counterbalance gravitational contraction.
But it turns out that if you actually examine the tail of the Maxwell-Boltzmann distribution at 15 million degrees, there still isn't enough stuff at a high enough energy to overcome the classical Coulomb barrier. It was at this point that astrophysicists realized that you don't actually have to overcome the classical Coulomb barrier; you could just simply quantum-tunnel through the last bit of it. In any single collision, this only rarely happens, but the density at the core of the Sun is high enough that it makes up for the deficit and explains how the Sun is able to hold itself up at such a low temperature.
A: You are not comparing like with like. Nuclear fusion in the Sun is extremely inefficient, generating just 250 Watts per cubic metre at those temperatures.
For nuclear fusion to be viable as a terrestrial energy source it needs to proceed much more quickly and hence requires higher temperatures.
A: For self-sustaining nuclear fusion burn, energy analysis results in the so-called Lawson criterion which is a necessary condition for self-sustaining fusion burn (ignition),
$$
n \tau \geq L\left(T\right)
\,,$$ where $n$ is the plasma density and $\tau$ is the energy confinement time.
The right-hand side is a function of temperature $$
L\left(T\right) = \frac{12 k_B T}{E_{\text{ch}} \left<\sigma v\right>}
$$where $E_{\text{ch}}$ is the energy of charged products of fusion reaction and $\sigma$ is the fusion reaction cross-section, and it depends strongly on the kind of nuclear reaction used, i.e., H+H, or D+T etc.
For any particular nuclear reaction, $L\left(T\right)$ would have a minimum (where the reaction cross-section $\sigma$ is maximized) which is the best operating point. It turns out that the reaction D+T allows achieving the smallest possible $L\left(T\right)$ at its minimum point ($\sim {10}^{8} \, \mathrm{K}$ in this case). Therefore D+T reaction and ${10}^{8} \, \mathrm{K}$ temperature is mainly considered today for designs of fusion devices (including inertial-confinement fusion, i.e., weapons), using this fusion reaction at this temperature makes the easiest conditions for achieving self-sustaining fusion (or ignition).
However, if a system size is large, then the confinement time $\tau$ can be huge, and then self-sustaining fusion burn can be achieved using fusion reactions other than D+T, and not necessarily operating at the minimum point of the corresponding function $L\left(T\right)$.
So, the key difference between the Sun and currently considered human-designed fusion devices is that the large size of the Sun allows achieving self-sustaining fusion burn using a fusion reaction with a low energy production rate.
A: Pribably_someone's answer is fine. I just want to add here a link that is useful in understanding the mechanisms, since comments might disappear without warning.

In order to accomplish nuclear fusion, the particles involved must first overcome the electric repulsion to get close enough for the attractive nuclear strong force to take over to fuse the particles. This requires extremely high temperatures, if temperature alone is considered in the process. In the case of the proton cycle in stars, this barrier is penetrated by tunneling, allowing the process to proceed at lower temperatures than that which would be required at pressures attainable in the laboratory. 

italics mine

The fusion temperature obtained by setting the average thermal energy equal to the coulomb barrier gives too high a temperature because fusion can be initiated by those particles which are out on the high-energy tail of the Maxwellian distribution of particle energies. The critical ignition temperature is lowered further by the fact that some particles which have energies below the coulomb barrier can tunnel through the barrier.

