Actually, reading and studying the Doctor's Opinion, and then how the terms and ideas are used in the book, I do think there is a difference between craving and obessession. And I think it is intentional.
It is as described above. . .mental obssession occurs before drinking. A craving is a physical reaction once an alcoholic has taken alcohol.
Now, having said that, does it matter? Not to me so much, as I know I have both. I work to control and eliminate the mental obssession so that I do not take a drink, thereby preventing my physical craving from occurring. This keeps me sober.