I thought a bunny was like a small rabbit または something. It could be a baby rabbit, too. It is also what little kids call rabbits and it sounds cuter. The words are spelled different, too. BUNNY and RABBIT. See? <3 :-)
I think bunnies were originally meant as baby rabbits, but now most people say either for the same thing. Although i think bunnies are probably imagined to be smaller and fluffier XD
Rabbits' ears stand up straight - sort of like a hare. And, bunnies' ears flop to the sides. At least, I think that's correct. Now if あなた compare this to that cartoon character, "Bugs Bunny," I think they called him that because it sounds better than, "Bugs Rabbit." So.. That's all lol