That's a good question. I remember when I was still getting used to my bf having a girlfriend, I asked if they had pet names. He calls her "monkey" and she calls him "papa". Despite the slight stab of jealousy I felt at the time, I had to admit that that was adorable.
I've started calling my new bf "baby" but my first/primary bf has always been "baby love" (he makes me want to sing that Supreme's song all the time
) When I fell in love with my new bf (a process that's still going on) I had strong urges to call him "baby" but thought it might be disrespectful since my first bf and I use that name all the time. I asked my first bf if he called his gf "baby" and he said yes, so that got cleared up pretty fast.
needless to say, If bf1 called me "monkey" I'm sure there would be problems, just like if I called bf2 "baby love" ahhhh....the intricacies of romance!