Think of it this way, an aid is a way to get a change. Whatever you do when you communicate with your horse, you are asking for SOME kind of change, are you not? So, in actuality, anything that gets a change from your horse can work and be called an "aid".
However, over the centuries, certain ways of applying aids, and certain aids have been proven to work the best. The goal in horsemanship is to reduce the use of aids to the quiestest that still works. When you start, in order to get the change that you require, you may need to use a big aid, coupled with the smaller aid. Over time, you stop using the big aid and rely on the smaller.
Ok, kind of drifting there. But my point is that a horse responds to a kiss for canter only because it was trained to do that. But probably, it was initially the rider had to tap it with a crop or touch it with spurs or kick with heel AND kiss to get the change. Then, they just kissed and it worked. My friends horse has no idea that "kiss" means canter. You must use leg on him. And, really , most horses associate a clucking sound or kissing sound with just "move more forward, more fast!" So , if you are just standing there and you kiss, they might move off at a walk or trot only. But, it's a "change", right? And that's what an aid does.
As for applying the leg, yes the horse is trained to move away from leg pressure. But in dressage one would have the leg laid passively against the side of the horse on the INSIDE of the turn. Then, the outside leg may have some more active application, such as gently bumping or tappling or just pressing in rythm with the horse's step, or a brush of the spur. Some kind of active movement of the leg that creates the reaction of "move" away from this. That inside leg laid passively against the side is meant to be more of a support, meaning "don;t just fall away from that outside leg aid, but kind of come to this passive leg and wrap your torso around it".
As for trotting and cantering. Hm m For me, I tend to use one leg application for "go!" in most any gait, but I know it's not textbook. IF the horse is walking too lazily, I might apply each leg alternately, with the swing of the horse's barrel. With canter, both legs go on, but one more active than the other, and in trot, I tend to want to apply the inside leg a lot more than the outside.
But, it just depends on what gets a change with a horse. That is what I am after. If it takes a whip to get a change, then that's what I use.