Paul Graham writes:
“Wise” and “smart” are both ways of saying someone knows what to do. The difference is that “wise” means one has a high average outcome across all situations, and “smart” means one does spectacularly well in a few. That is, if you had a graph in which the x axis represented situations and the y axis the outcome, the graph of the wise person would be high overall, and the graph of the smart person would have high peaks.
The distinction is similar to the rule that one should judge talent at its best and character at its worst. Except you judge intelligence at its best, and wisdom by its average. That’s how the two are related: they’re the two different senses in which the same curve can be high.
So a wise person knows what to do in most situations, while a smart person knows what to do in situations where few others could.