Hi Tricycling!
Triathlons are usually categorized by distance - ie Sprint (short distance), Olympic (middle distance), Half-Ironman (long distance) and Ironman (really freakin' long distance).
Within each race, the race organizers often have different categories and may choose to score those participating on mountain bikes separately from those riding road bikes, etc.
USA Triathlon is the national governing body for the multi-sport disciplines of triathlon, duathlon, aquathlon and winter triathlon in the United States.
Other sources of tri info:
Triathlete Magazine
Inside Triathlon
Hope that helps!