I find it hilarious either way.
No, I don't think there's much of a distinction in the U.S. Just a bit of an implication about how much InDiViDuAL ReSPonSiBiLitY there was in you losing your job. Like if you apply to another job and your prospective hirer asks you why you left the old one, if you tell them you were "laid off" they'll probably think it was mostly a "structural problem" at your old employer (though there's still a bit of a question of why you were laid off and not some other person), whereas if you told them you were fired (usually you just don't) they'd be asking a lot more questions and probably just turning you down without much more consideration.
Though also if the place which "lays you off" immediately hires someone in the same position, you might have some small chance of going after them for wrongful termination (usually only if you can also tie it to likely discrimination of some sort). Usually such lawsuits are a waste of your time and energy, though, as they can take years, are severely weighted in companies' favor, and rarely have any kind of satisfying outcome even if you "win".
I'm not sure "cheeto" is a good nickname now that Genocide Joe has gotten the ol' spray tan treatment as well. LOL. We're going to have to start asking "Which cheeto?"