Okay, I know nothing about 'natural horsemanship'. I don't really know anything about any particular training method and have no on-the-ground experience with them. However, from loads of reading and seeing others discuss this sort of thing, I would hazard a guess at defining a distinction.
It's important for a rider to be able to communicate with and understand their horse, and use techniques for this that avoid cruelty and get the point across clearly. For many riders, this is 'common sense'.
However, many of these 'natural horsemanship' trainers and instructors offer a programme that guides you through these techniques and offers suggested schedules and training routines. It is an aid to learning about these technniques.
Now, these programmes can vary in their quality: they may teach you the steps but not the essential reasoning behind them, they may have a huge commercial venture attached, they may be marketed with gimmicks or as applying to every horse when they do not.
In some cases, these programmes can be seen by their aficiandos as all-encompassing methods for training their horses. Others, however, see them as a non-exclusive aid. Or, indeed, as rubbishy gimmicks that do not actually help a rider or horse.
You have hit it pretty well! IMO, I think this would fall more to the aspect of the NH trainers that are more well known. But I did want to support one important thing you stated that is key..
use techniques for this that avoid cruelty and get the point across clearly.
Along with the cruelty aspect, the point of getting the point across is detailed better then what has been with a lot of traditional training techniques. I will add however, that in these "programs" most still lack the detail of "why" in "getting the point across" in depth. The "how" physically is discussed, but more importantly is understanding when each responce is understood by us. I think that would help many who are new into the equine field. There are too many people who will buy into a program and still not fully envelop the understanding of the horses responses. So if they could beef that up a little more, then you would have much more perspective into the training.
From reading your post, I am to assume you are not overly enthused with many of the popularized NH out there? LOL! I have to agree that yes, there are too many gimmicks applied to their programs, but I guess they need to make money too.
I think whats basic about NH, is understanding and applying good training, with minimal negative impact to the horse with the minimal amount and application of tools. Many out there become dependant on "needing" this tool and that tool for this and that, and before you know it, theres something new out there we need to get to do that too. I think this is where NH differs from many other types out there. Sadly, yes, there are a few of those "icons" out there that emphasize purchasing their "tools of the trade" to accomplish NH training.