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.