If I say dish rag, I mean something smallish you clean dishes with. Dish towel is larger, you dry with it. That's also what I think of when I sear tea towel, but a tea towel would be...fancier in my head.
I've been corrected on saying "dish rag" because you should say "dish cloth" as rag implies something negative apparently. I guess. I dunno, I've always said rag and think some people can be a bit too nit picky and look for things to be offended by.