The ABAB, etc, I'm familiar with doesn't have to do with rhyme or lines but with tune structure and customary playing. For instance, if one thinks of A as being the verse and B as being the chorus/refrain, sometimes A may be played twice before B is played for the first time. That would be called AAB. Perhaps, after that, B would be played each time; that would be ABAB.

That's a simplification, of course. Most tunes don't have choruses but do have a secondary tune in another block.

It is not rare for a tune to have four separate tunes or blocks, which, imo, are named A,B,C,D. For instance, the fiddle tune Dill Pickle Rag is often played A B then A C D then back to A to finish.

YMMV