First: there isn't one big difference. There's about 6 small differences that add up to be a big difference.
1. The mustang roll. Quite possibly the most noticeable and/or well known part of the natural trim is the mustang roll. Essentially, a mustang roll involves rounding the entire perimeter of the hoof.
2. Lower (shorter) heels. In order to promote healthy frog health and development, it must have some ground contact. Thus, the heels are trimmed lower so that the frog comes as close to touching the ground surface as possible.
3. The natural arches of the horses foot are allowed to remain (the area called the "quarters" is shorter). The hoof is not designed to be flat, and it shouldn't be forced to be.
4. The frog and sole are NOT trimmed unless absolutely necessary. This is something that traditional farrier schools usually do teach, but does not work well for barefoot horses. Horses need to be allowed to build up a strong thick healthy sole and frog if they are going to be comfortable barefoot.
5. Removal of flares. Even if there aren't huge obvious flares with splits and chips, many horses have some degree of flaring that needs to be addressed.
6. A backed-up (not "shorter"!) toe. Trimming the toe too short from the bottom up is often what causes post-trim soreness. It's important to keep the toe backed up from the front to keep the lamina strong, but not to trim the toe too short from the bottom of the hoof.
Now, as a final caveat:
It's possible that you may be thinking: Well my farrier does all of that, but he doesn't call himself a natural trimmer. To that I will repeat a quote that a wise farrier once told me a long time ago...
"A good farrier is a good farrier is a good farrier. I don't care what you call yourself; I've seen bad farriers and bad natural trimmers... And I've seen old farmers that could trim the lamest horse around and make it sound."
You decide where to take it from there.
