The distinction between “heavy drinker” and “alcoholic” is mostly an AA thing, and it’s entirely notional. There’s no hard line in the sand, on one side of which you’re a “heavy drinker” and on the other of which you’re an “alcoholic.” There are only degrees of difficulty in stopping. It’s a continuous spectrum, on one end of which are those who drink a lot but can stop without difficulty, and on the other end of which are those who die from their affliction despite every earnest effort to stop. There’s a lot of middle ground there.
I don’t find this made-up distinction useful, as can encourage people in AA who identify as “real alcoholics” to accord themselves a weird kind of elitist status.
If you self-identify as simply a “heavy drinker” who wants to quit, well, go ahead and quit. If you try to quit but have any difficulty doing it, you can call yourself anything you want as far as I’m concerned, but you're welcome to ask for help here -- it's what we're here for.