A mole is Avogadro's number of anything. Nature certainly is redundant. But the really remarkable thing about the redundancy of nature, is that it is truly redundant. Not at all like the hairs on your head, each of which has a slightly different shape and length from every other one. No matter how hard you look at it, no matter what you do to it, it will behave in exactly the same way as any other carbon atom that you do the same thing to.
Some carbon atoms have different nuclei than other carbon atoms.
To be really precise, I should say that all carbon atoms with 12 nucleons in their nuclei are completely indistinguishable. But that doesn't change the idea. That is one of the strange things about physics. We don't know much, but the things we know we know very well. But I am getting sidetracked.