saddle seat is for gaited hotse. They ride with a long sturp. They do not post.
Not necessarily true. While some gaited breeds do ride under saddleseat tack, many trotting breeds do saddleseat on a large scale, such as Morgans, Saddlebreds, Friesians, Arabians, National Show Horses, Dutch Harness Horses, Hackneys, etc.
When riding saddleseat, your horse shifts back and gets under himself while raising the neck and freeing the shoulders to lift higher. Saddleseat has several divisions (within trotting breeds, and I will explain the ASB divisions as well), in Morgans, these divisions are Classic, which is in general, the least knee action and is limited to amateur riders. The class is nearly the same in ASBs, but these horses can only be keg shod, and it is not limited to the amateur rider. This is called Country Pleasure. Same name in Arabians.
The middle division, in Morgans and Arabs, is English Pleasure. These are the the mid-level knee action horses. This is comparable to three-gaited pleasure in ASBs.
The gaits called for in Classic and English Pleasure in the Morgan world are the walk, trot, road trot, and canter. The walk is a flat walk.
The highest stepping division in Morgans, Arabs, and ASBs is Park. These horses are powerful, high trotting, and hot. The classes called for, at least in Morgans, are the park walk (it is not required to be a flat walk), the park trot, and the canter.
There are also driving classes that are saddleseat-type. In Morgans, these are Classic Pleasure Driving, Pleasure Driving, and Park Harness.
ASBs also have a 5-Gaited division, which is walk, trot, canter, plus slow gait and rack.
Equitation in saddle seat is fairly simple in concept, but often very difficult to learn when you are used to hunt seat. A saddleseat rider sits at the back of the saddle, often leaning slightly back or perfectly straight up. The knee and toe of the rider should be aligned. Hands are held higher than they would be in hunt seat.
Here is a video of a Morgan classic pleasure class:
And here is a saddleseat equitation video: