Simple answer, it doesn't. Now 60fps to 120fps can make a difference. Lower input lag, smoother image depending on the viewer. But 60fps at 60Hz or 120Hz would look identical. The screen would either shift down to 60Hz or draw each frame twice.
I'm getting too old for all these frames per second. When I was young everything was measured in frames per minute I remember playing at about 300fps on my old CRT at 800 x 600, the refresh rate was set to 155Hz. It felt smooth, but no smoother if I'm honest than 80fps did at 2048x1536.
So you were really playing at 155fps lol Smoothness, as I've said many time is down to the individual. As is input lag to a certain degree. I remember trying to buy a monitor that did 2048x1536 and my local computer shop couldn't get me one so I gave up
