For well over 70 years folk songs and the pop and rock songs that
followed them used the terms "verse" for the part of the lyric this
isn't repeated, and "chorus" for the repeated part. Your mistake was
only in the narrow context of Broadway tunes of a certain period. I
think they did away with this by the 60's.
The reason Ira Gershwin called it "the vest" was this: It's not a
jacket, it's not a shirt, what the hell it is it? It's the totally
superflous and unnecessary part.
And as sheet music proves, it is as thoroughly forgotten as a publisher
can make it.