baby is another word for "fluffy little woodland critter". Teenagers use it to refer to their loved ones as cute and cuddley without offending them by calling the "bunny boo" or "chipmonk face".
Remi: Ciao, babe! See you tomorrow!
Marisa: Eww, you sound like a beatnik! And don't call me a baby !
Remi: No, I said 'babe'!
Marisa: Oh, okay. That makes sense! See ya babe!