I have no interest in getting into a heated debate, but here's my take on natural trimming. It is more than a name or title; it's a different way of trimming barefoot. I believe that how horses hooves are trimmed has a whole lot to do with them being able to go barefoot or not.
In the case of my horse, his hooves wouldn't hold a shoe and even after years of being barefoot, he still wasn't sound over a hard-packed dirt or clay road and certainly not over gravel. After approximately two months of natural trimming he was showing a great improvement. He's now been totally sound for well over a year and I don't regret switching to a natural trimmer at all. He moves better as well...collection and extension are much easier for him and his back has gotten stronger.
I also have a friend who's old jumper gelding had always had to wear shoes and could never be sound barefoot. When she finally decided to give natural trimming a shot, he was sound barefoot in just a few months and she was amazed.