I think the confusion arises from many people saying they "crave" alcohol, when what is actually going on is that they think about it a whole lot.
In AA, thinking about booze a whole lot, is called the "mental obsession " and the "physical craving " is the part of alcoholism that ensures that we never stop at one or a handful of drinks.
So in AA we say, we have a two fold problem.
Mental obsession will eventually drive us back to drink, physical craving / allergy ensures we cannot moderate once we commence drinking.