The original definition of a slim taper neck was one that varied in thickness (front to back) from the 1st fret to the 12th by only 1/10 of an inch. It did not mean the neck was "skinny" or small. The neck on the 1960 Les Paul is barely any thinner than the 1959, in some cases 1960 LPs measure the same as some 1959 models. But this was the first appearance of the "slim taper" and it just meant that the neck didn't get much fatter as you moved towards the body of the guitar.
Unfortunately Gibson started using the slim taper with many of their necks, and the idea that different models would have different sized slim taper necks due to the fact they were different guitars was overlooked/ignored, and people just called every neck that was thin a "slim taper" neck. Also Gibson have changed their neck profiles over the years and within the same model lines. Then you have the Japanese who started copying in the 70s and would have been confronted with a baffling range of neck sizes to check. Greco seems to have used a fatter 1958 profile for most of their high end clones, Tokai went for a few different profiles including 59 and 60, but seemed to have settled on 59 profiles all the way for the current guitars.
It has led to a lot of confusion.
My own Bacchus Duke LP has a fat neck but it does not get much fatter at the heel, so it would very likely be called a slim taper neck, but it is not a small neck believe me.
