That may be an accurate description of hunt seat classes in breed shows, but hunt seat or hunter seat is a discipline of and into itself, governed by the USEF and the USHJA. It is based on the principles of sound cross country riding over fences, following hounds, but has evolved into a distinct show ring discipline. It is characterized by a forward way of going, a stirrup short enough to allow the rider to get out of the tack in two point position and light, passive contact.
The version that is practiced in breed shows has evolved into some different and distinct from actual hunt seat. If you do a Google image search Hunters on the flat, Hunters over fences or Hunter Seat Equitation, it will be immediately obvious which photos are from breed show hunters and which are from traditional hunters.
In short, the definition of "hunt seat" goes way, way beyond what happens in breed shows.
I agree, and I hope I didn't offend anyone. And when you said "It is characterized by a forward way of going, a stirrup short enough to allow the rider to get out of the tack in two point position and light, passive contact." I was trying in my own weird way of saying that.
There's definitely more than one definition of huntseat, it just depends on the context. It's been my experience in the Midwest that it's more common to be called huntseat when stock type/TB types are involved, like at breed shows, open shows, and 4-H. Whereas english seems to refer to the breeds that have more "action". For example: At our county 4-H, when the kids sign up for huntseat pleasure classes, the horses tend to be judged more on length of stride/forward movement, and the horses tend to me more solidly built (if that's the best way to describe it), where the english pleasure classes they like to see the kids with the Morgans, newer type Arabs, etc. basically the ones that have more action and can be described as finer boned. Right or wrong, that's just what I've seen.
It's kind of like showmanship, I've seen it being judged strickly on the handler, or judged on the horse. Just depends on where you live, and what discipline you're involved in.