HID is high intensity discharge. its just an acronym for that type of light.
Projectors are the housings. they have a glass lens in the front. thats the peice that looks like a glass sphere in there. regular headlights just have a reflector in the back and no lens upfront. its just the clear plastic piece on the outside of the headlight and you can clearly see the lightbulb in there.
xenon is the gas they put inside the light bulbs for HID lights that emits the glow.