Games and education, whats the difference?

The more I think about "Education" and "Games", the more ambiguous I find the distinction. Typically both are abstract systems with an imposed set of rules based loosely on some subset of reality. The number of players can vary from 1 to indeterminate, and we often have an abstract value system, which is used to rate players/students on their performance.
I’m just finding it hard to come up with a unique distinguishing feature for which I cannot find a counter example.