Theoretically, could there be different types of protons and electrons? Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something else. That doesn't make sense to me! There are different types of apples, but they're still called apples!
He says that's how protons work, but can we really know that?
 A: Almost none of the other answers, as good as they are, include a reference to more massive versions of the quarks and electrons. 


Theoretically, could there be different type of protons and electrons?


Below is a diagram of the standard model, which imo, the post is also implicitly asking about. The chart leaves out the anti-protons (really anti-quarks) and anti-electrons, which do exist with opposite electrical charges to their otherwise ordinary matter "twins".
Up and down are the lightest varieties of quarks. Somewhat heavier are a second pair of quarks, charm (c) and strange (s), with charges of +2/3e and −1/3e, respectively. A third, still heavier pair of quarks consists of top  and bottom , again with charges of +2/3e and −1/3e, respectively.
These heavier quarks and their antiquarks combine with up and down quarks and with each other to produce a range of hadrons, each of which is heavier than the basic proton. For example, the particle called $\lambda$ is a baryon built from u, d, and s quarks; thus, it is similiar to the neutron but with a d quark replaced by an s quark.
The proton is formed from two up quarks and a down quark.
But a particle made from the top and bottom  quarks, which would be the analogue of a proton, in the third generation of quarks, cannot be formed. The reason is that the top quark is so heavy that it decays to a bottom quark by weak interactions far more quickly than it can form an (even extremely short lived)  proton-like particle.

It may not jump out at you at first, when you look at this list, but there are 2 more versions of the electron, and 2 more versions of each quark.  The reason we don't see them in ordinary life is because they are more massive than the standard quarks and electrons, so when they are produced in high energy collisions such as at the LHC,  they decay quickly (that is they have a very short lifetime). The extra short lived  particles are the muon and the tau, and the extra quarks are the strange, charm, top and bottom.
A: Your friend is correct: there's only one type of proton.
The proton is the lightest baryon. It has charge $+1$, spin $1/2$, and baryon number $+1$. 
These three quantum numbers are so fundamental that if you try to change any of them, the result won't be a proton. For example, if you change the charge to $0$, you get the neutron, and if you change the spin to $3/2$, you get the $\Delta^+$ baryon. If you change the baryon number to $-1$ (and also change the spin to $3/2$), you can get an anti-$\Delta^-$ baryon.
We could call all of these particles excited states of the proton, but this wouldn't be useful, because they behave so differently: the different quantum numbers drastically change what processes they can participate in. For example, the $\Delta^+$ can decay to pions and nucleons, and the anti-$\Delta^-$ can annihilate with normal matter, and so on.
Perhaps the most important feature is that the proton is stable, because there's nothing lighter for it to decay to. This is an extremely important property (it's why protons are in nuclei instead of, say, $\Delta$ baryons), and none of the other baryons above share it, so it makes sense to let "proton" denote the unique lightest, stable baryon.

The case of the electron is easier. It's a fundamental particle, so it can't have any excited states by definition. The closest thing to the electron is a muon, but that particle is so different that it's in no sense a 'different type of electron', as I show here.
A: Apples is a category. Particles is a category as well. Golden Delicious and Pink Lady are specific unique types of elements in this Apple category. If a Pink Lady was different, we would have called it something else. The name Pink Lady is much more narrow and is only given to apples with those exact features.
Protons, electrons etc. are unique types of elements in the Particles category. The unique features in protons is given the name or defined as "protons".
If the features were different, it would have gotten another name. Maybe still in the Particles category, but different from the proton since we only defined a very specific set of features to be called protons.

Don't be confused about there "only being one kind" of something. That just means that the specific name/term, you are talking about - like the proton - is just defined very specifically/uniquely.
A: It is an experimental fact that all electrons and also all protons (but this often applies also to nuclei, atoms and even molecules) are indistinguishable from one another, i.e. they both are identical particles.
Imagine to perform the following experiment: you take two objects A and B, perform as many measurements as you want on them, put them into a "black box", shake the box and then take them out. At this point, you want to be able to tell which object is A and which is B.
Let's say that A and B are two...apples. You can then measure their mass, their volume, take photographs of them etc.: you will obtain different results (taking into account experimental errors). Therefore, the only thing you have to do is take note of these results and you will be able to tell which is A and which is B.
However, if you try to do the same thing with two electrons, you will discover that all the quantities you can measure (mass,charge,spin etc.) are identical within experimental error. Therefore, you will not be able to tell one electron from the other.
This is an experimental fact, and as far as I know there is not a theoretical reason why it should be so. Maybe one day we will be able to perform more precise measurements and we will discover that electron charges are actually slightly different from each other!
PS I would like to stress that it is pointless to say that protons are identical because they are made of identical quarks, because this only shifts the problem from proton to quarks (we could then ask "why are all quarks identical?").
A: A proton is made up of 2 up quarks and 1 down quark.  These quarks must be one of each of the quantum chromodynamics colors (red, green, or blue).  This leads to a constant charge across all protons that have been observed.  So starting from that point, what characteristic of a proton would you suggest that we modify and still call it a proton?  And what about that particle would still mostly act as a proton sufficiently to be called a type of proton, with some slight variance in the resultant physics?
Unfortunately, in the current standard model, there are nothing that indicates that there are different types of protons.
A: An elementary particle is defined by quantum numbers. If two particles have identical quantum numbers it means there are no distinguishing features that separates one from the other. This means electric charge is the same, isospin number the same, other gauge charges (color etc) are the same and the more complicated mass eigenvalue is the same.
Let's imagine a situation where there might be two different types of protons and see informally where that leads us. In the multiverse we have different cosmologies with different internal gauge field and particle structure. Let us consider a putative cosmology with the same elementary particles. Yet because gauge charges and the rest are different a proton, or really quarks etc, and maybe leptons such as electrons have different masses. In a multiverse situation we might then be tempted to say there are different protons!
I like Feynman's original idea of the path integral, which is that an electron is on a path that zig-zags and buzzes around both through space and back and forth in time. This means all electrons and positrons are the same particle! There is fundamentally only one electron in the entire universe. We might think of the vast multiplicity of electrons as having been frozen into place by the occurrence of the cosmic particle horizon, and the appearance of many of them is a sort of holographic illusion. In the case of the multiverse we would than have any particle state zip-zapping across different cosmologies, and so different protons in other universes are just the same proton as protons here. We might think of particles in other cosmologies as having a renormalized mass, just as an electron has mass renormalization if it passes through a crystal of condensed matter. The different vacua of different worlds would be analogous to putting the electron in crystals that renormalize the electron mass. So we then might have trouble stating with certainty, at least until theory and better yet measurement falsifies this Feynmanesque idea, that protons can in any fundamental way be different.
In the multiverse setting we also have the problem that we may not be able to ever cross into another cosmology and make this comparison. Maybe in the Susskind et al ER = EPR setting the comparison can be made in the interior of a black hole. there a black hole is a sort of nontraversable wormhole with the Einstein-Rosen bridge connecting two different worlds. Susskind pushes this further to have it connect with many worlds in a sort of wormhole "octopus," as he sometimes calls it.
In QM there is indistinguishability of particles with bosonic and fermionic statistics that goes along with that. I would then say that until demonstrated otherwise this is pretty fundamental. 
A: The key to the answer is observation. We have already observed a lot of small and huge things interacting with each other.
Unscientific answer would be: there could be a multitude of subtypes of a proton, but we simply haven't invented yet the experiments which show those subtle differences.
Scientific answer is NO. Per Occam's razor, if we found a particle that interacts the same way, always and in every experiment, then we are safe to simply call it a proton. That's it. Period. The Scientific Method is to always use the simplest theory. If you are using a more complicated theory, personally I call it "unscientific method". It doesn't mean you're necessarily wrong; but surely your theory lacks elegance. The classical argument is Carl Sagan's story "The Dragon In My Garage".
A: There are two ways to distinguish particles: you can either measure a difference in the intrinsic physical properties of the particles - say mass, for example - or track the trajectory of each particle with infinite precision.
Since a proton is always formed by one d-quark and two u-quarks, every proton has the same mass, charge and spin. The other possibility is contradicted by quantum mechanics, specifically the Heisenberg uncertainty principle.
It seems that your friend is correct, then. In fact, since you can't distinguish protons, it's possible to say that every single proton in the universe is the same!
A: you are merely arguing semantics. your friend is right because there is no way to distinguish one proton from another.  you are right because we might some day find a way to distinguish one proton from another.  you two seem to be arguing about what words we would use for the two different types of proton we might someday distinguish.  
we might call them both protons (e.g. "this is a type 1 proton and that is a type 2 proton"). or we might come up with a new name for one of them (e.g. "this is a proton and that is an experton, which is exactly like a proton except...").  which way the language evolves probably has to do with how common the two different kinds of protons are.  if all the protons on earth are type 1 protons, then we will probably give the type 2 protons a new name, but if earth has both type 1 and type 2 protons in equal quantities, then they will probably both still be called protons. you might say that when we discovered antiprotons, we had this exact choice to make.  it seems we chose to give the particles a new name because all the protons on earth are type 1 (protons), not type 2 (antiprotons).
A: There are in fact 2 types of Protons - Protons and anti-Protons.
They interact and behave exactly the same way and are completely indistinguishable from one another. However they will mutually annihilate on contact.
Other than that refer to the other answers here. If a particle looks like a Proton, acts like a Proton, reacts like a Proton - then it's a Proton.
If you have a particle that shares some similarities with a Proton (e.g. a previously unknown stable Hadron that has a positive charge); but is different in some way - mass, charge quantity, etc... well then it won't be called a Proton, it would be called something else.
A: I believe you are arguing semantics.  To make this clear, lets assume there are only 200 type of "particles," each with a unique set of properties.  Once we give each one a name, there can't be any more of "the same thing" with a different name.  For example, lets say that number 12 on this list we call it "electron" and number 125 we call it "proton" then, any particle that meets the properties of #13 must be an electron, and those that meet the properties of #125 must be protons.  Since there are only 200 particles, if a given particle does not have the properties of an electron (12) or a proton (125), then it must meet the properties of some other particle on the list (neutron, positron, neutrino, etc.).    
