The beige pants are called "breeches" (pronounced Britches). And by top, do you mean a helmet or shirt?
The shirts are button down with a mandarin style collar that you attach a decorative pin to (for show jumping) or a tie. For dressage, they wear a shirt with a Cravat style tie called a "Stock Tie".
Both wear jackets over the shirts. Jumpers wear blazer style jacket with 3 buttons. Dressage riders wear a jacket called a "Shadbelly" (for higher level) or a blazer style jacket with 4 buttons. A Shadbelly ends at the belly and has tails.
As for helmets, both show jumping and lower level dressage wear Velvet riding caps. High level dressage riders wear a low crown top hat.

