Welcome, Clearwrite!

I've just been checking random copies of my sheet music collection (19th century through to 1950s), and the 'introductions' are labelled "verse" (as Kupatchka noted). The other part of the song was labelled, variously, "chorus" or "refrain".

And I agree that many "intros/verses" are gems (Stardust, in particular, and most of the Gershwin songs).