I'm a western person, and as was mentioned, it's all the same thing. Dressage is just training the horse and rider. I was watching the first part of the Olympics dressage, and pretty much patting myself on the back. There wasn't a thing that they did that my mare and I couldn't do (bareback or western, hackamore, curb bit or snaffle). Everyone used to comment about how they couldn't see the cues.

She reined like a QH (although she was mostly TB) and could spin and slide with the best of them. It was all about getting the most bang for your buck. Minimal cues with dramatic results.

So why was I patting myself on the back? I was 13 years old when I got her (green) and trained her to do all of this myself. Personally I think this should be the goal of any horseman (horsewoman). Horsemanship, that's what it really is!