It's a vague and useless question, with at least two answers.

1) There might be some tradition of contrasting "strong AI" projects to make an artificial person and "weak AI" projects to compute something smartly, but the former do not exist in practice.

2) If they play against each other, the strong AI beats the weak AI.

2b) More importantly for game design, a strong AI is frustrating because it's too good for human players, while a weak AI is boring because it can be fooled without serious player effort.

Feel free to do your own homework, Chris.

Informally I think you could describe the difference like this:

- the weak AI can figure out what the solutions are to a specific problem

- the strong AI can figure out what the problems are in a given general situation, and then solve them

In the context of games you have http://en.wikipedia.org/wiki/General_game_playing algorithms, that would be able to play *any* game, as opposed to a specific game.