This was fun! I like the term "echo song" for when singer 2 just repeats (Supping Cider), and if call-and-response or challenge-response works for the one where a chorus chimes in, I feel I have answers. I got the term Challenge-Response from computers.

Lining, however, I think of as something different, as a subset of Echo. I read about lining in To Kill A Mockingbird (still the best book ever written in English, I think).

Next question: Is the distinction between a Refrain and a Chorus the number of people joining in? That is, is a set of lines repeated after each verse by a single singer a Refrain, whereas if the band joins in to sing those same lines, it's a Chorus?