One of the things I try to impress upon my students in my Principles of Micro and Sports Econ courses is the difference between self-interested behavior and selfish behavior. When a person acts in his self-interest, he is making a choice because he feels he'll be made better off. But when a person acts in a self-interested manner, he can intentionally make others better off as well. In other words, a self-interested person A may take another person B's well-being into account, but A does so because it makes A better off.
On the other hand, when a person acts selfishly, he does not take others' well-being into account. He makes choices because they make him better off, others be screwed.
Consider a basketball player who needs one more point to be the all-time scoring leader. It's his last game and if his team wins this game, they will be champions. They are down by 3 and there is 10 seconds remaining. If the player looks only for his own shot merely to get the scoring record, then he is acting selfishly.
If, on the other hand, he passes the ball to open teammates with better shots than he has, potentially sacrificing the record for the better of the team, he is acting self-interestedly and not selfishly.