Hi Perish64oh... A bunny is a baby rabbit, just like a kitten is a baby cat and a puppy is a baby dog. Technically it is not correct to call the adult animals "bunnies" but there are instances where the common name for a small rabbit species is something like "brush bunny". And of course people do still call their dogs, puppies and their cats kitties and their rabbits bunnies... ;)
rabbit is a universal translation. If someone is just learning English, they won't understand that word, "bunny." Rabbit can be translated into all languages, well, except for places where rabbits don't exist.