Now you made him confused, where's the facepalm smiley. You had it right, it's refresh rate. The rate at which the buffer refreshes.
It depends on the game as far as the fps lock goes. But that issue aside, more fps is less input lag and you'd see the action ms before others with lower fps. When you go above 60 fps on a 60hz, you lose the benefit of seeing the action earlier since you can't see the extra fps but input lag would still be less.