The Wikipedia article on rabbit breeds lists two groups American Rabbit Breeders' Association (ARBA) & the British Rabbit Council (BRC).
Are these the only two groups for defining rabbit breeds?
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Groups like the American Rabbit Breeders and The British Rabbit council work in a way similar to dog breeders associations. For instance, the American Kennel Club recognizes breeds differently than the Continental Kennel Club. Each association has different breeds that may or may not overlap and may not have similar standards. In order for a new breed to be recognized a breed club will form and then create a working standard that the association may or may not recognize.
That being said, breeds such as the Lionhead rabbits are not recognized by the ARBA (American Rabbit Breeders Association). This rabbit is still considered a breed just not recognized at this time. So these clubs do not define breeds, it is the breed club that defines them. Once they wish to get recognized, they will need to work with a parent club such as the ARBA to come up with an agreed upon standard in order to get their breed sanctioned. The lionhead and other rabbit breeds are currently working on ARBA recognition. For instance, one can still show lionhead rabbits at a show if they bring a working standard with them to the show.
The ARBA and the BRC are the largest all breed rabbit associations and are often the governing bodies for hundreds of smaller regional clubs. If your questions is more based on whether the standards created by these clubs are guides for rabbit shows. The answer is yes, most rabbit shows will use either the ARBA's Standard of Perfection or the BRC standards. They do not define the breeds, the breed clubs do that.