In my own head, I mostly unpack "smart" as being able to effectively reason with a given set of data, and "wise" as habitually treating all my observations as data to reason from. Someone with a highly compartmentalized mind can be smart, but not wise. If (A -> B) but A is not actually true, someone who is smart but not wise will answer B given A where someone wise will reject A given A.

That said, this seems to be an entirely ideosyncratic mapping, and I don't expect anyone else to use it.