Well.... When I was young & new to horses, I got into Parelli.... in hindsight, rather fanatically :roll: I effectively programmed myself with his recommended exercises and was able to then retrain my old thrasher, who didn't take kindly to the conventional style of horsemanship, or the pain from a bit used harshly in a very sore mouth(cheeks were literally red raw when I got him :( )
In hindsight, while Parelli taught me an awful lot, the way I was doing it, with knowledge of the techniques but without much 'savvy' of the principles behind it, it wasn't very 'natural' & often not overly pleasant for my horse. I was able to get him to do just about everything I asked of him, ride him out with just a string around his neck, etc. But try as I might, I couldn't get him to WANT to be my partner, to enjoy being ridden.
Then I discovered c/t & studied behavoiural psych. The world again opened up to me! As you've said, the name is a bit of a gimmick, and as with Parelli, while people often get hung up on the equipment etc, it is the principles that are important. If you understand & follow these, you understand that the clicker, food treats, carrot stick, etc are just helpful tools, but are in no way necessary. With c/t I was able to teach my boy(& others who have come after) to actively enjoy playing my games, whatever they may be. I think this is near impossible if you're only using negative reinforcement.
I now use a combination of methods. I still predominantly use NH style exercises & negative reinforcement, but use a lot of positive reinforcement too. It has been great and helped me with the many people & horses I've trained in the last years.