This is really where you need to seperate your thinking between the video signal and the production of the picture.
The video signal is a fixed refresh rate, governed by the source (computer, dvd player, sky box, whatever) and the capability of the viewing platform (tv, monitor, projector). Your monitor will be capable of certain rates, and the computer (gfxcard) will be capable of others (usually 100s at different resolutions), they compare notes when they meet via a dvi cable or whatever, and where they agree you have a list to chose from. 120/100/75.. blah blah. Replace the tv for the monitor and sky box for the computer and the basis is the same. If they compare notes and nothing matches, you get no picture.
... but your game will still be playing @ 30 or 60 fps.