I like your definition of alcoholic. I feel the same way. I am an alcoholic because I can never just have a drink or two. It's like they say, once you start you can't stop.
As for relapse, well, I am not so sure how to define that for other people. In my experience though after any amount of time with out drinking if I give in and talk myself into "just one more night of fun" its all over. Back to the drawing board.