Neil deGrasse Tyson recently stated that 'creativity that satisfies and affirms your world view is entertainment. Creativty that challenges and disrupts your world view is art'.
If we apply this logic to filmmaking, then Stanley Kubrick managed to tow the line between the two in the most transfixing way possible. Kubrick was a huge, blockbuster filmmaker. His films made incredible amounts of money for their respective studios, while also often receiving great critical acclaim. But his films were never what one would call easily digestible.
Even what should have been his most easily-commercial film, The Shining, was something that challenged many viewers and critics alike. It was despised by critics initially. He had taken the fairly straight-forward narrative of Stephen King's novel and distorted it in a way that only Kubrick could. This was true of all of his best films. From 2001 to Clockwork Orange to Eyes Wide Shut, Kubrick specialized in making high-art films that were constantly requiring the active viewership of its audience.
Stanley's films received a whole lot of nominations, but the only Oscar any of them ever won was for Best Visual Effects in 2001. Kubrick remains an all-important name in the history of filmmaking and the fact that he never won Best Director is utterly dumbfouning.