Western riders do post however we do not show posting. More of a training tool. Good way to get a feel for your horse and it also really helps teach your horse to rate.
If they are true beginners there is very little difference in what they need to know. To sit properly heals down keep their legs still and so on. Make them drop stirrups just like you would with an English students. Big thing is holding the reins properly. I see this so much in both western riders as well as English riders. They do not hold their reins properly and have a hard time keeping soft hands b/c of it.
At the beginning beginner level, much remains the same - particularly with a dressage seat. There are more differences with a jump seat. Heels under hip is stressed less, and many kids ride too large saddles that make it hard to have the heels back anyways (I'm thinking my youngest daughter, who weighs 85 lbs but rides a 16" saddle because that is what we have).
My daughter in law is older, but she was taught sitting the trot in her first lesson. From observing, I'd say there is more emphasis on being able to stop the horse quickly and completely, and more emphasis on having fun while on the horse. I took some group lessons in my teens. IIRC, the second half of the first lesson was on a trail. Looking back, I don't agree with it, but that was how it was done then.
I really don't understand the purpose of "western dressage". Western dressage is reining,not slapping chaps on the rider and Western saddle on the horse. Also, judging by these pictures, some of these horses have to be confused out of their minds because their riders are trying to ride with contact with a curb. Curbs are not meant to be ridden with constant contact.
I'm certainly not going to put a jumping saddle on my mare and run barrels, then call it English barrel racing..
I expect my Western horse to bend around my leg on circles and serpentines, so I don't understand this statement.
B/C that is not the norm. Western horses are trained to move away from pressure. Now in doing that they can and do bend around your inside leg but a circle at least in reining is a bunch of small straight lines not one big circle.