What's the Difference?: Athletics, Sports, and Games

What is the difference between games, sports, and athletics? While surely not all games are sports, can we say that all sports are games? Not all athletic activities sports, but are all sports athletic activities? What about competitive ballroom dancing? It is a competition and physical, but is it a sport? Is it a game? Are the dancers athletes? How about body building? Is it a sport? A game? If so, would that make beauty pageants sports? Surely, the contestants train for it in similar ways. There is strategy involved. But it doesn't seem like we should call the contestants athletes, or should we?