English, I see as dressage/showjumping/XC etc. Anything that uses a basic english saddle or one of its modifications and based around the english 'seat'. The US 'hunt seat' style would come under this too.
Saddleseat is so radically different - both in tack and rider position - it just bugs me to see it classed as 'english'. That's no slight on it, of course, it's just a classification that bugs me, no matter how 'correct' it may be.