Absolutely. Every horse is trained slightly different. Every horse, as an individual, is slightly different.
A good rider will adapt to the horse and cue the horse in a way that will give them the best response.
I used to have a horse that was trained "backwards" for his lead changes. For a right lead, you'd push him over with your right leg. Therefore, when I rode him, THAT'S what I did. Because that's what he knew and as a rider, I adapted to him.
When I ride a young horse that doesn't know how to neck rein, I obviously have to ride two-handed. When I ride my horse, he'd neck rein no problem with just my legs and the halter.
I think it is very education and very beneficial to improve your riding skills by riding as many different horses as you can. You will have to adapt slightly different to each and every one.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.