Having learned how to make saddles, both "english" and "western" style, and having looked at saddles through the ages, I've found that all saddles come in two types, based on the tree.
The older type, which has been used for many centuries, is based on placing two shaped boards parallel to the horses spine, resting upon, and extending back past, the horse's ribcage, joined by two arches, one forms the pommel and one forms the cantle.
(four-point) saddles, Mongolian, Chinese, Sarmatian, medieval,
Hungarian, British Army U.P. Saddles, the McLelland Saddle, and Western
saddles all are based on this pattern.
The newer type, developed in the XVIIth Century by the French cavalry school, is built on a single board suspended above the horse's spine by an arch in the front and a Y-fork at the rear, which also supports the cantle, This saddle rests on four heavily-padded points that sit on the horse's ribcage.
Dressage Saddles, European riding saddles, the Australian Stock saddle, and, most especially, the Caprilli-Style jumping saddles are all based on this pattern.
The benefits of the parallel-board saddles is it distributes the rider's weight across a larger area of the horse's back, which allows for longer rides or more weight, wearing armour, carrying equipment and so on. Even so, the wear on the horses is such that they need rest to recover, even though they do go farther than foot-soldiers in a day. The Mongol invaders typically had 3 horses each, so each warrior rode one horse, had packs on the second, while the third rested, and they swapped places every day.
Moreover, the amount of lateral stress put on the horse is distributed across the whole spine, so activities such as jousting or roping cattle can really only be done on this type of tree.
The drawbacks of these types of saddles, however, is they are inflexible, and so the horse has less agility and freedom to move. Heavy saddle-blankets and padding are necessary, which makes the saddle very hot to wear for the horse. It is relatively difficult (not impossible) for the horse to jump or cross obstacles, as the bascule is blocked by the stiff boards and the jarring on landing is very hard on their backs.
The benefits of the suspended board on points is it allows for exactly the agility required of horses to jump over high fences and to ride quickly across rough country with much less stress on the back.
The drawbacks, however, is the saddle cannot carry very much in the way of weight beyond the rider for any length of time. The saddle must also be re-stuffed at least once a year, preferably more often, to ensure the points are not weighing down and creating pressure spots. Fitting to the horse is a very precise art to ensure that the horse has the freedom to move while in balance.