In the English saddle world, there are basically four types of saddles: dressage, close contact (aka forward seat or jumping saddles), all-purpose and trail saddles. Which saddle you choose will depend on the discipline you'll be riding.
Since some people want a "do it all" saddle, and some aren't sure what discipline they want to pursue, all-purpose saddles are fairly popular, especially with beginners. Most a/p saddles should be ridden with a moderately bent leg (think of the front of your thigh lying parallel to the front of the flap), which will allow you to do a little jumping (small fences), a little dressage (lower level) and flat work; they're comfortable and secure enough for a trail ride. They often feature a deepish seat, a moderately forward flap, and a round cantle. Some, like this Black Country Summit, have a straighter (or VSD/dressage focus) flap:
And this is a Frank Baines Enduro LDR, which has a slightly more forward flap and deeper seat (and does show the dees):
These saddles also often have a crupper bar attachment in case a crupper is needed to help stabilize the saddle.
Some trail saddles have extended panels, which means that the panels extend (obviously) quite far to the rear. This does maximize the weight bearing area, but can be problematic on shorter-backed horses like Arabs (which, ironically, are the most popular breed for endurance and competitive trail).
Next, let's look at the close contact/jump/"hunt seat" saddle. It has a flatter seat, a square cantle and usually a more forward flap; you will ride in it with quite a lot of bend in your leg (again, imagine the parallel between the flap and your thigh), since the focus of these saddles is jumping and riding in your two-point rather than sitting.
And this is an older Stubben Tristan, probably German-made:
These old saddles didn't offer much in the way of luxury and cushiness; the leather was usually quite slick and the knee rolls/thigh blocks were usually tiny or totally non-existent. You weren't helped to stay aboard with big blocks or deep seats or soft, grippy leather ...
(As we fade to black, the old dinosaur saddle fitter is waxing nostalgic, remembering with fondness and a tear in her eye the longe-line lessons with which she tortured her students, and their feeble cries of protest when she made them drop their irons ...)