On the face of it the terms book smart and street smart simply differentiate between people who went to university and those who figured it all out on their own i.e. attended the school of hard knocks.
But I suspect the term book smart is a kind of shorthand used to describe people who think they're clever but lack a reasonable degree of common sense. It's a thinly veiled derogatory term used by the street smart folk to refer to those whose academic credentials are insufficient to compensate for a general gormlessness.
According to Is It Better To Be Book Smart Or Street Smart?, an article which possibly misses the undercurrents associated with the respective terms, people "without advanced education will likely say that they've done just fine without spending a lot of time in the classroom, while people with a lot of formal academic knowledge would say that success is largely the result of education". The piece lists people - Steve Jobs, Steve Wozniak, Bill Gates and Richard Branson - who have succeeded without a college degree. However it also states that unemployment statistics "show book smarts more than double your chances of finding a job".
Urban Dictionary says a street smart person "has a lot of common sense and knows what's going on in the world". The implication is that it's edgier and far cooler to be street smart, living on instinct and gut feelings, than a formally educated nerd.
