There are around 370 different ways to prove the Pythagorean Theorem, but what does that exactly mean? For instance, if your proof states that $x^2+y^2=z^2$, I could construct a different one by claiming that $a^2+b^2=c^2$. On the other hand, some proofs just take a different turn or a shortcut at one step (often arguably the same), others could almost be considered corollaries of more generalised ones but, still, are considered to be disjoint.
I hope we can at least agree that changing the names of the variables of a proof wouldn't make it different, but then here goes my question: where do you draw the line? Is there some sort of equivalence relation that classifies the types of proofs or is it just something vaguely subjective, all in all?