I didn't want to obfuscate my response further, but there are even more types of Western saddle (I've never been a big user of Western saddles, so it's not my forte). Notwithstanding, there are Western saddles designed specifically for roping, barrel racing, training, endurance, trailriding, and all around. In the briefest terms, these are deliniated by the tree (framework upon which the saddle is built), ruggedness of the horn, height of the cantle, weight, and turnout of the jockey flap and fender. Somewhere along the way, I even saw a Western saddle with no horn at all -- I think it was used in bronc riding (in rodeo), probably to help prevent the male competitor from exiting said event with a soprano voice.
I could go even deeper into this fascinating subject because not all horses/breeds are created equal. For instance, Arabian horses have one less vertebrae in their backs than other breeds, making them shorter coupled and often necessitating saddles that are built on modified trees. Typically, saddle trees are constructed of wood and wrapped in thin wet rawhide, which dries as a very tough membrane around the wooden tree. Other parts of the saddle are then attached -- skirt, seat, pommel, cantle, jockey flaps, fender, stirrups, etc.
Sims 3 Pets seems to make no distinction among saddles, except vanilla English saddle, jumpseat English saddle, racing saddle (flat, very small English saddle), and a rather ubiquitous Western saddle.
