The different styles were/are developed by the different artists just like painting, then as they become popular their style gets copied. A lot of it is the business side too on the more modern styles at least and probably why you thought it started in the 40s, Stohlman for example started about that time and as he got better he started to produce tools and books and made it a business which promoted his style further. It makes it troublesome to some degree as the tools we can buy were created to do a certain style well but we as artists/humans also want to develop our own style as we get better so we either have to make do, learn to use them differently or develop tools we need ourselves. At least that's my take on it.
Leather carving IMO is influenced by centuries old traditional methods, folk art/ untrained leather workers embellishing personal items, professional artists/people making a living at it and every thing in between.