Distinguishing games, serious games, and training simulators on the basis of intent

What's the difference between a game, a serious game and a training simulator? Unfortunately we don't have a zippy punch line for you, but in this work we present a means to segregate the three on the basis of user intent and the closeness to their reality, rather than the intent of the designer. We use analogies to older educational media and their classification to illustrate our point.