Probably not helpful, but I'm starting to think it's the age from the many things I've read lately. DS is 20 months too, and while he's fine on poops, pee normally goes on the floor. He'll comment on it while he's doing it, or call me when he's done to help him clean it up, but he doesn't go and sit on the potty by himself. He'll go if I take him to the bathroom, but he doesn't initiate either. I have been having those days lately where gradhood feels oh-so-far-away! However, I have often heard of this stage refered to as the one last horrible potty strike before the end, so I'm hopeful that's what it is.
I don't know about your DD, but DS is in a very "toddler" stage right now, which I think is due to his canines coming in...they're not in yet but from all our other experiences with teething he seems to have his teeth move around in his gums for a long time before coming in. He's very moody and inconsolable and tantrumy lately. His new thing is that he very deliberately pees on the floor when he's mad and that's the end of his tantrum. I'm not sure if he expects us to get upset or something? Lol. I'm always impressed when he does it because it shows me he does have the know-how and control!
Anyway, that was a long answer just to say that it sounds like your DD is a typical 20 month old, and that things might change very soon! You're not alone, anyway!
Mama of two... DS born at 35w5d (11/06) and DD : born full term 38w3d (5/09) on what would have been my dad's 64th birthday. Always missing my dad who died of oral cancer 3/11/09.