I can answer that question for you!!
Quad tap means there are 4 available .. um .. "tap" configurations (tri tap is another commonly used ballast, then double and single-tap). What this means is there are 4 ways to power the ballast: 120 VAC, 240VAC, 377V and um .. I think 480 is the last choice.
Quad taps seem to be the most common AFAIK. I assume this is because they are the ones produced in the most volume maybe. Basically depending on the (industrial) application the line voltage may be one of several things and it depends on different things.
Basically for our use, we're really interested in the 120 tap only. I imagine one could run ballasts on a 220 circuit intended for stoves and dryers although I don't know if there'd be any real advantage, although I've often wondered about that.
PS. According the EYE Lighting website, even the EYE ballast is a combination halide/mercury ballast...
http://www.eyelighting.com/ballastmercury.html (notice the ANSI column has both M numbers and H numbers for each ballast)