Projector, Reflector, Halogen, and High-Intensity Discharge (HID) are all different types of heaglight. Projector and Reflector both describe the headlight housing, and HID and Halogen describe the type of light emitted.

Reflector
First off, let's start with the Reflector headlight. Basically, a halogen (HIDs can be retrofitted) bulb shines in all directions. There are reflectors (basically shiny plastic) surrounding the bulb that direct the light in a general forward-and-down pattern.



Projector
Now, what exactly does a projector headlight do differently? More or less, it does the same exact thing as a reflector-housing headlight, with the addition of a condenser lens placed at the front of the light. The lens directs the light into a much more specific pattern, putting more usable light on the road. Also, projectors usually have cutoffs to keep the light from blinding oncoming drivers.



Halogen bulbs really don't require much of an explanation... they more or less work light a normal light bulb

HID headlights (also known as xenon headlights) uses an electric arc passed through xenon gas to produce light. Generally they're brighter and better than halogen lights, but they come with a higher cost, too. For the record, most oem HID lights are between 4000K and 5000K.


Also, it should be noted that most projector headlights have a projector light for the low-beam and a reflector light for the high-beam.

*images pirated from wikipedia... fair use ftw

 

oh ok that clears up a lot, thanks!