Yeah I've always seen it and heard it referred to as the repeated bit of (usually) the chorus or lead line of a song. They're very popular in Broadway tunes and things like that.
For example, there's a tune called (I think) "This Could Be the Start of Something Big" sung by Pia Zidora (among other people I'm sure). (I'm not a big broadway fan, but I know this tune because it was featured in Naked Gun 33 1/3!)
The end of each verse of the song ends with "This could be the start of something big." I think it's kind of a chorus, but not really. It's more of an A-B form, like "Yesterday." "Yesterday" doesn't really have a chorus, but each verse is capped by the line "I believe in yesterday" (or something similar).
Anyway, in the "something big" tune, that's the way it happens the first few times. But at the end of the song, it goes:
And this must be the start of something...
This could be the heart of something...
This could be the start of something big!
That's the tag. The chords usually change a bit for each repetition of the line. In this case, I think the first and last line have the same chords, but the middle line has different chords (that would lead to the first chord of the third line).