Didn't this happen with horse riding? AFAIK they had different names for different areas of their sport - eg. racing, show jumping, trials, trotting, dressage etc. All different sports in their own rights.
Not quite like that with equestrian sports Raffles. There are 2 main bodies that cover just about the whole lot - the British Horseracing Board which covers racing type events, and the British Horse Society which covers eventing, dressage, showjumping, polo, mounted games.......... Then there are committees and organisations under each of these 2 main bodies such as the BSJA which regulates showjumping.
I think also that most of the "traditional" sports were recognised long before the Sports council came up with the latest "qualifications" for recognition, so don't need to be run in the same way as the newer sports.