I'll add to what ru12 said.
One might think of 'willpower' as choosing not to drink/use, one desire at a time. The Big Plan, however, removes the Option of choosing one way or the other, and solves the addict's Shakespearean dilemma (to use or not to use).
The second difference from what is usually thought of as 'willpower' is in the use of recognition, and attribution, to maintain separation. I want to use, but I won't use, for example, is not AVRT.
"IT (my Beast) wants to use, but I never use", in contrast, is certainly AVRT. The separation extends to feelings around using, such as "drinking feels good" (For whom? For my Beast.)
As long as the expression of the addiction (the Addictive Voice) is recognized and attributed, so that the addiction remains an IT somewhere "out there", it loses its perceived power.
If this is difficult to visualize in practice, consider that we do this all the time when reading, for example. As I read your posts, Morning Glory, I am hearing a voice in my mind's ear, and it sounds a lot like my own voice. As I read, however, I recognize that voice in my mind's ear, and attribute it to someone "out there" who goes by the name of Morning Glory.
That voice I hear in my mind's ear, as I read your posts, which sounds very similar to my own voice, is not mine, but rather, that of Morning Glory.
AVRT is somewhat like that in practice.