I think the distinction most people are making when they talk about street and book smarts is that street smarts is your social savvyness while book smarts is how knowledgeable you are. How socially savvy you are is much more dependent on your ability to act well immediately in different situations while your knowledgeability is more passive and intimately tied to what you learn from books; usually implicitly being perceived as theoretical knowledge instead of practical. From a social perspective, a book smarts person knows much but is less accurate in the way they apply that knowledge while someone with street smarts isn't necessarily knowledgeable but their use of what they do know is skillful and comes off as natural. But when a book smart person applies their knowledge and ability to learn in mastering the social arts, and succeeds in that regard by having a wide spectrum of experiences and developing killer instincts through them, someone like Chase is born.
Best,
Oskar