Some TVs can do native 100/120 inputs, but it's rare. What they do is accept a 50/60 signal, and repeat the frames internally, for instance. 24p (24 Hz) blu-ray content is going to repeat each frame 4 times as the TV will run at 96 Hz. On a 120 Hz TV, it's repeated 5 times, and the refresh rate remains the same, where as on a 100 Hz TV it's lowered by 4 Hz. This is to get rid of telecine.
Now here is something important to know, that a lot of people don't quite understand. If you have a native 100/120 Hz TV, or native 200/240 Hz TV, then that is a fixed/static rate, meaning there is no extra input lag added by processing the frames. The result is far less ghosting, regardless what FPS a game is running at for instance.
However, you won't get smoother game play, as that requires more frames to be displayed, but isn't possible, so you're only getting 50% of the advantage of a higher refresh rate. Same goes for monitors.
Regarding cables, it's always best to stick to digital when using it with a TV, because HDMI doesn't support all resolutions and refresh rates just because it's got the bandwidth for it. VGA is old, and will reduce picture quality depending on interference and length, as well as the quality of the cable.
Lastly, only HDMI will do HDCP handshake when used with a TV, probably some exceptions but HDMI is the standard. DVI can't do it, neither can VGA.