Yes - the alcohol is a symptom of the addiction. A normal person can have a few drinks and not think anything of it. Go home and not think about alcohol for the rest of the night. An alcoholic becomes obsessed with getting more and more with none of the self-control you would practice in any other situation.
For example... If someone invited me over for cake, I can't imagine eating the whole thing, even if I wanted to. But I would, and have, drank entire bottles of expensive wine, almost all my friend's Grey Goose.... The next day I would feel horrible. Thats why an alcoholic should never pick up even one. Not even a sip.