Paraequestrian is the name for riding associated with people with a disability.
Currently the majority of the riders are involved in dressage, but there are groups which are competing in carriage driving and show jumping.
The only difference here in the para-athletes is that some equipment may be allowed, or that they may only ride at a certain pace (walk only, walk-trot only etc)
Many riders with a disability do compete in general competitions, but this is the special discipline which allows them to shine amongs peers.
Riders compete according to their Grades which are an indication of their physical capabilities. This is predetermined by a doctor or physiotherapist that has had training and is an Official Classifier.
====From Official WEG Website====
The para dressage discipline provides riders with physical disabilities the opportunity to compete in high performance equestrian sport along side able bodied riders from all over the world. For the first time in the history of equestrian sport, para dressage will be included in the World Equestrian Games in 2010 held in Lexington, Kentucky, at the Kentucky Horse Park. The experience of qualifying for and competing at the highest level offers each rider the chance to represent their country regardless of their disability