Ummmm, I would say that if they take it out of the Atkins book, its Atkins.
Ketosis (which Atkins diet seems to be) is recommended in some circumstances for various reasons. I know of one man (and he might be a freeper) that used the usual low fat diet and got to a point where he just could not lose any more body fat. Atkins diet was his cure. He's a powerlifter himself, but as a hobby, not by profession.
In the bodybuilding circle, ketosis dieting is often cycled utilizing various patterns such as 5 days on, 2 days off.
I fear that we may begin to split hairs here. I'm only recommending keeping an open mind WRT diet. I don't buy everything that the WHO recommends, that's all.