It is BOTH smart stay and smart rotation.
With smart stay on (and smart rotation off) if I set my screen timeout to a short interval, like 30 seconds,. I notice the eye pop up just before the screen dims, and again just before it shuts off. If I'm looking at the phone, when it pops up the it'll reset the timer to 30 seconds, at which point the above will repeat.
If I turn smart stay off (and smart rotation off), the eye never pops up, and the screen shuts off whether I'm looking at it or not.
With Smart Stay off, and Smart rotation on, the eye pops up sometimes when I rotate the phone.