You have it partly right. Let me explain (and probably overcomplicate matters as I do so).
I don't think I've ever seen the Forum song called anything but simply "Invocation." That's what Sondheim calls it in Finishing the Hat, and I think it's been called that everywhere else I've seen it specifically mentioned (at least by people who know the history). The Frogs song is usually just called "Invocation and Instructions to the Audience," although on ovrtur, our first of several variant titles is the longer one starting with "Prologus," as that is what was in the original published script. If memory serves, there was no list of musical numbers in the Yale program, although I wouldn't swear to that without double-checking, which I can't do right now. Anyway, "Prologus" does not refer to the first part of the song but to the whole song. That version of the title is "Prologus: Invocation and Instructions to the Audience," which is what you wrote but you also seem to be thinking that the opening part is "Prologus and Invocation." The whole song is the Prologue to the show.
Anyway, all that made its way from Forum to The Frogs was, as you suggest, the opening, introductory section of "Invocation." The bulk of the cut Forum song titled "Invocation" is not in "Invocation and Instructions to the Audience," which is largely a completely new song.