Sort of - my point was that the actual aids for SI and HI are the same in terms of how you use your legs, hands, even seat - it’s a matter of how much of each and the riders intent that make the difference whether the horse is travelling in SI or HI/HP.
I was thinking about this thread last night while doing my horse’s most hated exercise - trot, canter, trot transitions. She’d rather not go back to Kindergarten, tyvm lol. “This is a BABY exercise. We should only do WALK, canter, WALK!” Anyway, when I was pretty new to riding, let alone dressage, I was very lucky to take weekly lessons plus “Saturday Club” at the stable I rode at. Extra lucky was that there were serious dressage riders including a very well-known judge who boarded there and who were roped in to give occasional mini clinics at Saturday Club.
One of the mini clinics that really sticks out for me was the longeing clinic they held. Not only did we learn how to longe properly, but we got longed on various school ponies. The Most Important Exercise I ever learned was during that clinic. We had to walk trot and canter, both up and down transitions, with no reins and no help from the person longeing. That really cemented into my brain that ANY* horse can follow the lead from a seat changing its motion AND most of all - we are responsible for maintaining the gait we want with our seat no matter what the rest of our body/aids are doing or whether the horse is saying, “This would be a lot easier if we just changed gait.”
*The school horses were Joe Bought At Auction Grade Horse types who gave lessons to riders of all levels from rank beginner up and mostly were ridden hunt seat by more advanced riders, they were not schoolmasters of any type, let alone dressage schoolmasters!