There are also distinctions that only exist for someone to flout[1] their superior knowledge of the technical terms. That is a social status issue, not a matter of precision.
Best example of that case would be collective nouns: "oh gosh, you're supposed to say a "crash" of rhinos; you can't just say a "herd" or "bunch"! ~adjusts monocle~
Best example of "precision matters and can cause confusion" would be "literally" or "biweekly". It causes confusion when people can't rely on X-weekly meaning "X per week" or "every X weeks". You would be majestically justified in prodding people to stick to the same convention to avoid confusion.
But there any scenarios where "signature vs invocation" actually matters to the point that you would do the wrong thing as a result of someone ignorantly flipping the terms? The only thing I can think of would be if someone said, with no other context, "change the parameters to fix the bug".
[1] I know, it's "flaunt", not "flout". That's the point: they don't compete for the same semantic use cases, so they don't cause confusion.
You might think to yourself "Surely this parameter/argument thing is such a fundamental bit of terminology that it would apply to all languages?", to which I'd point out that there's an entire paradigm to which this distinction doesn't, strictly speaking, apply: Concatenative languages. Further, in Perl 5, functions and methods don't really have "parameters" at all. (Prototypes permit some optional, complicated, and generally not used stuff.) Also, in a language that permits equational reasoning it's not clear to me that the distinction has the same meaning, though I'll concede that's a more subtle point.
I'm not aware of very many terms that can be strictly applied across all languages. Even something as innocuous as "int" has significantly different semantics in different languages (does it roll over or transparently upgrade to a BigInt?). You could call it a "machine int", perhaps, but that terminology isn't necessarily what I'd call "common use" even if most people will know what you mean.