A heavy drinker is someone who drinks a lot.
I was actually being polite and saying problem drinker when I meant alcoholic, but I would say that both of those mean someone who HAS to drink a lot.
Example - when I was 22 I was in a distance relationship. We both drank massivley, even more so when we were together - even then we would easily manage more than a bottle of wine each per night, plus i would often have a couple of pints during the day. I think that we both therefore drank a lot and were heavy drinkers.
Anyway, we split up, not over the drinking per se (at least, we didn't think so at the time ...) but we clearly weren't happy and wanted different things. She got a very high-powered career (which she still has) and, while she didn't stop drinking, she didn't let it get in the way of excelling at that career. In other words, she drank less, and she put it second to the rest of her life.
I put drinking first and fucked my life up royal, to the extent that, as an Oxford graduate who had been destined for an academic teaching and research career, I moved back in with my mum and struggled to hold down a job as a shelf-stacker.
It turned out that I wasn't just a heavy drinker; I was a problem drinker too.
Now this doesn't mean that alcoholics can't succeed in business or the professions. Many do, not least because they tend to be driven to succeed because they often have something to prove. What it does mean is that drink will always come first - if they're not sacrificing work, you can bet they're sacrificing something else, quite often the feelings and safety of those who love or depend on them.
It's akin to the difference between a small eater and an anorexic, a social drug user and a coke addict - when it comes to the crunch, can they change, or will they stick to what they know and damn the consequences?