What's the difference between a sport and a game?

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I think any activity in which the layperson can practice every day, for 12-14 hours a day, for an extended period of time (couple years?), and turn around and put up a good fight against a 'pro' in that activity, is not a sport but a game. In other words, if I put a couple years or a decade of dedicated work into football I still wouldn't be able to cover a NFL wide receiver, or any other task associated with football. I doubt I'd be able to hit a 95mph curveball either. However, I think I could average in the upper 200's in bowling with a little bit of practice. I think golf is another example of a professional activity that is more of a game, than it is a sport. What do you think?