This is a big question with no easy answers. Both problem drinkers and alcoholics have found that alcohol plays a negative role in their lives. It can cause difficulties that include, but are far from limited to relationship dysfunction, job loss, and social embarrassment. Yet, what is the difference and how do you know which applies?
First off, both the problem drinker and the alcoholic need to address their drinking. However, the problem drinker should have an easier time of it. The Big Book of Alcoholics Anonymous addresses this very issue. It asserts that problem drinkers are able to stop or moderate their drinking for a sufficient reason, such as health or to keep a job. Problem drinkers are also able to moderate their intake if the situation requires it. Thus, they might appear to be mild or moderate drinkers at the office party, and they might even refrain from drinking when they don't have a safe ride home. However, once they are free of external restraints, they will drink to their heart's content.
Alcoholics, on the other hand, have been known to drink until they breathe their last breath. They will cry out for a drink, though booze has sent them to their deathbed. Alcoholics also find that once they start drinking, they are incapable of stopping. As the Big Book describes the alcoholic, "he is seldom mildly intoxicated."
One way to tell if you are a problem drinker or an alcoholic is when you try to stop drinking. Or, in the words of the Big Book, attempt to "drink like a gentleman." Though that language is antiquated, the authors mean that, if you are able to drink a moderate amount and then stop, you are probably not an alcoholic. Likewise, if you pledge to stop drinking for a period of time, such as a month, you can fulfill that pledge if your drinking has not yet crossed a certain line. Keep in mind that these informal assessments demand that you be rigorously honest with yourself. That's because, if you are still craving and obsessing over alcohol after you drained the evening's last glass, you might have a deeper problem.