Fogg's claim is narrower than most advice about habits, and the narrowness is what makes it usable. Behavior is not one lump of willpower you either have or lack. It has three inputs, and the model's real assertion is about timing: they have to land together.
Written as a formula, that is B = MAP. Behavior equals Motivation plus Ability plus a Prompt, converging at one instant.
One wording note, because it trips up anyone who reads two sources on this. In the 2010 Stanford talk quoted above, Fogg calls the third element a trigger, which is why the older form of the model is written B=MAT. He later renamed it prompt, and the current form is B=MAP. Same element, same model, newer word. If one page says trigger and another says prompt, they are not disagreeing with each other. His definition of the thing has not moved either way:
The second half of the model is the trade between the first two elements. Motivation and ability compensate for each other along a threshold Fogg calls the action line. Enough of one covers a shortfall in the other. A behavior sitting above that line fires the moment the prompt arrives; below it, the prompt does nothing except make somebody feel bad about themselves. That gap is the difference between behavior design and a motivational poster. The poster tries to shove you over the line. Design moves the line.
Three inputs, one moment, one threshold. That is the entire model.