experience alone does not produce wisdom.
Very true. Some people go right along repeating mistakes / digging deeper holes, etc.
Wise is a word we use to describe other people whose combination of intelligence and decision-making we admire. I can't say this is universally true, but anecdotally, it would ironically seem the wiser the person is the more likely they are to downplay their own wisdom, or to point out the limitations of that wisdom (like Socrates).
While intelligence and experience are components, the nature of wisdom would seem to be rooted in action (or lack of action when appropriate); perhaps good decision-making would be the simplest-- if broadest-- summary of what being wise is about.
From there, we could make two slightly less broad distinctions: 1) External: wisdom with regards to making decisions and acting based on understanding one's environment and the other players one is engaged with in one's environment in order to achieve a given end (think Machiavelli, Sun Tzu, etc.); and, 2) Internal: wisdom with regards to making decisions and acting based upon understanding and controlling oneself... to "know thyself" as the Greeks and others used to say, which is the development of equipoise and diligent reining in of erratic emotions and thoughts that lead to unwise or distracted action.