Often, education is directly correlated to intelligence in conversation.  It is fallacy that they are directly connected.  What is even less correlated is formal education versus intelligence.  Formal education is in no way related to intelligence.  It could possibly help someone, to have a good education or a good formal education, to appear intelligent.  But a good education does not make someone intelligent.

This is where the topic borders on non-political correctness.

Intelligence is, if anything, more of a genetic trait.  Education is not.  Education can be equalized in offering but not in acceptance.  Intelligence cannot be equalized in any way except through genetic manipulation and direct and indirect control of an infant through childhood upbringing.  We can to some degree control education, but we as a people can in no way control intelligence yet.

So when someone blurbs on, rather stupidly, about someone being educated or not educated, what they often mean is that they are or are not intelligent.  This is a kind, or faux sophisticated way, to say someone is or is not intelligent.  It's at worse a complete misnomer in concept and at best just entitling the declaring individual, less intelligent or thinking than they'd like to superficially provide.

Has this gone all sophisticated?  Maybe so, but there are mostly factual realities in these statements, with a slight bit of arguable philosophy.

In summary, intelligence does not equate to education and education does not equate to intelligence.

Period.