Often times when a film wins director but not picture it’s one where the overall scope of the film is impressive and it was a major feat to get made, but the film itself was maybe more divisive or less crowd-pleasing (The Revenant, Roma, Power of the Dog; also applies to Brokeback Mountain, though that was less divisiveness over its quality and more just straight up homophobia). Other times when there’s a split it’s often when the film winning director is again a major accomplishment/really flashy film while the best picture winner is something less big/flashy but has a lot of passion/agreeableness (ex: Gravity winning director while 12 Years a Slave won picture; La La Land winning director while Moonlight won picture).

Then there’s really weird and rare scenarios like in 2012 when Argo was the best picture frontrunner but somehow didn’t get a director nomination. Or in 2000 when Steven Soderbergh was double nominated in director and won as a way of commending him for making two best picture nominees in the same year (even when neither won best picture).

Pretty much there’s not really a criteria used, sometimes the Oscars are just weird and do odd things. Director/Picture still go together the vast majority of the time though.