The "we're so enlightened we don't even need money" conceit is basically an invention of TNG, even though one of the earliest pieces of "evidence" for a no-money Federation is a line from a TOS
movie (a line which really only implies that physical currency
is no longer used). There was plenty of money in TOS. Everything from "credits to navy beans," in fact.
Even if only considering TNG and later, though, -Brett-
pretty much has it right.