Sport & Game

Yesterday night before headed to dreamland, I asked my brother a question, "how to differentiate sport and game?"

I didn't get any answer, so I decided to look up the dictionary. It says:

Sport: an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment

Game: a form of play or sport, especially a competitive one played according to rules and decided by skills, strength or luck

Well, I still can't figure it out, as Olympic Games (a kind of sports event), or for instance, badminton game (a kind of sport too). I am kind of puzzled all a sudden.

My personal view to this would be, sport is a physical activity, while game can be in form of physical or intellectual activity. Although it's kind of lame, but, at least it's more acceptable, at least in my terms.