Only hibernate when closing the lid, display sleep otherwise? I am looking for a way to hibernate (i.e. RAM saved to HDD then turned off) only when closing the lid. When the lid is opened, I expect OSX to simply turn off the screen after X minutes (i.e. everything keeps running). Mostly what a Windows PC does out of the box.

pmset does not seem to make possible controlling what happens when closing the lid.
Hibernate only (not sleep) when closing the lid:

sudo pmset -a hibernatemode 25


And to go back to "normal" behavior: 

sudo pmset -a hibernatemode 3


As for the sleep behavior with an open lid, just slide the Computer sleep timer to Neverin System Preferences > Energy Saver. Alternatively do

sudo pmset -a sleep 0