There is quite a bit of information that can go with this. I have only had experience with Missouri Fox Trotters, Rocky Mountain Walking Horses, and Tennessee Walking Horses, and I have not been involved in gaited shows.
Tennessee Walking Horses have a flat walk, the running walk which can be quite fast, even up to 20 miles per hour, and the canter. Some have also been known to rack, and a few other gaits, but these are not seen in the show ring.
Missouri Fox Trotters are able to Flat Walk, Fox Trot, and Canter.
Rocky Mountain Horses are known to Walk, Single Foot, Rack, and Canter.
Now I am no where near a professional on gaited breeds, only my own experience. I really have no experience in the showing of gaited breeds.