To me, the type of riding you do is not about the tack, or the discipline... The way I think about it is the horses way of going.
See, to me, HUS is western riding. By this I mean the 'way of going' in a HUS class. If you rode like that at an english show here in AUS, you would not get a second glance and someone would probably laugh or b*tch. The way of going, with the low headset and super slow gaits, is not 'english' to me at all.
When I think english way of going, I think more of a dressage way of going. Not always that far, but more forward gaits, a higher headset... You couldn't go around a jump course very well riding like you were in a HUS class.
The only real difference I see between WP and HUS is the tack and the one handed/two handed reining.
I think labelling whole disciplines as one or the other is a bit exclusive... It gives the idea that if you don't have a western saddle, you can't barrel race, or chase cows, and if you don't have an english saddle, you can't practice dressage... Which is not true.
I would classify myself as english, I guess, but I barrel race, and I chase cows, and cut them from mobs etc, but I do it all with the 'english' way of going. Forward gaits, higher headset...
Hmm. Just my thoughts on the matter.