Hi Dutchie,
I went looking for a thread I saw within the last couple of months discussing differences between RR and SMART, but couldn't find it. Perhaps someone else will remember where it is and post the link.
At the risk of oversimplification, I'll give it a shot:
SMART approaches include cognitive behavioral therapy. What you think and feel about the challenges in your life is important in maintaining sobriety. Countering "irrational beliefs" and doing a cost benefit analysis of using vs not using are some of the tools used to help change your thinking to support abstinence. "I am not thinking things through clearly. If I look at my behavior rationally and accept myself with all of my foibles, I will be better equipped to handle urges to drink."
AVRT doesn't care about rationalizations, beliefs or analysis about any thinking aside from drinking. Recognize any thought that supports the possibility of drinking as having been delivered by your addiction and separate your true self (I) from the addiction (It). "I don't want to drink, It does, and It doesn't wear the pants around here. Too bad."
I am not familiar with WFS but did take a peek at their website. Seems WFS is more "like" SMART in that it focusses on change through positive affirmations (and presumably action to support the affirmations).
SMART's website has a toolbox that will give you a very good overview. The basics are straightforward, in my view.
If you haven't already done so, you can get the gist of AVRT by Googling it and doing the crash course.