The results of sitting deeply depend on what you're doing with your legs and your hands too. For example, if I sit deeply and squeeze my hands on the reins very briefly, and then reach back with my outside leg and touch my horse's side, he'll break into a canter. If I sit deeply and squeeze my hands on the reins firmly and take my leg off, he'll stop and stand still.
You talk to your horse with your seat, your legs, and your hands. Your horse feels every little thing you do with all three of them. If you squeeze your butt muscles even a little, he feels it. If you wriggle around in the saddle, he feels it. If you put both reins in one hand and scratch your ear, he feels it. It's like, in English, we have 26 letters, and those letters get rearranged and used over and over to make words, and then the words get rearranged and used over and over to make sentences, and ultimately, you can make a book.
Think of the different leg, hand, and seat pressures and positions as being an alphabet, and with that alphabet, you're "writing" requests that your horse can understand. He's a pretty good reader, so it's up to you to be a good writer. And just in the same way as I can describe something as a "crushing blow" I can mix up the signals and what I really say is a "blushing crow". Same letters, totally different meaning.
This, to me, is the hardest thing about riding well, learning all that stuff and keeping it straight. And I can *understand* it with my head, but still wind up doing it wrong with my body. That's where a good instructor comes in - that person can see what you are doing, and give you helpful suggestions about how to fix the part that needs fixing...without messing up the good part.
It's also why instructors will tell you that the aids need to be independent. That means that if you put your leg on, for example, it doesn't automatically cause your fingers to tighten around the reins. You may *want* to tighten your fingers on the reins, but that should be a decision, not something that just happens because you put a leg on. Having something happen with your seat just because you did something with your hands is how we get the blushing crow, above.
I know it's kind of long, but I thought it was important to be clear that it's not *just* sitting deeply that makes the horse stop...it's the whole package of stuff you are telling the horse at the same time with the other aids that combines with sitting deeply to make the horse stop.