Rabbits are what you eat, bunnies are what you pet.
Seriously, some people use "bunnies" to mean young animals, and "rabbits" to mean more mature animals, but it's the same animal. Mostly, "bunny" is just a cuter word, people tend to use "rabbit" when they are trying to sound more serious.
Rabbit is the general name for the species. Bunny is a technical term meant to refer to a rabbit of a certain age. I think that age is between the ages of 3 - 5 months. Most people don't use it like that anymore (I don't) but I know some 4H kids are sticklers for proper terms because they compete and take it seriously.
I've never heard of 'bunny' being a proper term for anything. Here's a short blurb on the history of the word, no idea how accurate it is: http://www.etymonline.com/index.php?term=bunny
LOL You know, I think you're right. I can't find any info in print of the use of "bunny" as a correct term for anything. I can't remember where I had heard it was but now that I think about it, I don't think I've ever heard of it being a question in any youth competitions. Never mind. Don't mind me any.