Refresh rates (not FPS game rendering, but screen output) is related to the frames per second being rendered by the game engine in the way that you need to have the refresh rate of the screen running at least at the same framerate of the game engine rendering to potentially see any advantage (that's why some claims regarding Call of Duty games running so much smoother are so horribly funny when you find out they are just running a 360 game on a slow refresh rate SDTV, or even worse when they point to videos encoded in less than 30 frames per second to prove their point, like on gametrailers). 
Refresh rate with certain technologies refers far more to screen flickering rather than fluid animation. Depending on the used display technology this is more or less relevant.
