To me, which may or may not be the correct definition it goes like this.
A job is a place where you go to get paid. You really could care less about the work you do or why you do it. You can do it well, but really all it is, is a paycheck.
A career, is a place you WANT to be. This may mean advancement, it may not. It's something you are interested in, and may even like doing. You strive to do your best because you feel it means something to you. A career is a place you get a paycheck, but if someone offered you a higher paying job, you'd stay where you are because it's what you really want to do.