In my mind, people mostly ask different kinds of questions when they are looking for wisdom. They want to know how to make their marriage work, or how to have a happy life, not the most efficient way to sort a list. And those questions tend to benefit from both a greater EQ, and extensive life experience.
Of course, there is such a thing as a "wise old engineer", but even there, what people are usually looking for aren't the technical details, but distilled experiential wisdom -- the "how to get started with so many unknowns" or "how do I navigate the treacherous politics of" or "how can I build a career when the things I'm gaining expertise in will be irrelevant in 10 years?" questions.
I think it depends on how you define "clever". Does knowledge of things like how to sort a list correlate with cleverness?
I know wise people who don't have formal education, but I'd still consider them exceedingly clever.
I built a wood shed many years ago. I looked up the recommended roof slope and used trigonometry to calculate the angles of my cuts. The next time I made one, someone with more wisdom showed me that you could simply assemble a flat roof with joists sticking out both sides, raise one side until it seems right, and then run a circular saw vertically along the side to create a neat edge.