If you consume so much alcohol that you become inebriated, you are drunk. If you do it too often, you may become a drunk, which is another, blunter, word for "alcoholic."
For the last 600 years or so, the word drunk has been used to describe someone who is intoxicated. Someone who's drunk from alcohol might be unsteady on their feet, slur their speech, or not be able to think straight. But you also can be drunk on things like power, passion or hope. This kind of drunk involves strong feelings or intoxicating emotions instead of one too many beers.