briefly:
projectors are a type of housing. It’s a curved convex lens that the bulb sits behind. There are typically light gates, or cutoffs, behind the lens, that give the light a nice straight cutoff.
Halogen bulbs are standard incandescent bulbs. You can get them in various colors, but nearly all of them suck.
xenon = HID. These are more kin to flourescent light’s as they need a very high arcing voltage, hence the need for ballasts and igniters. The current used for operation is less than halogen bulbs.
Bixenon is a way of saying the car’s hi/lo beams are both HID. Some setups physically move the light gate. (mechanical bixenon) There are also dual “filament” hid bulbs, where the luminosity actually increases based on electrical input to the bulb.
CHeck www.hidplanet.com or www.hidforum.com