Headlamps is a light at night, industry known as 'light'.
Headlamps have general lighting, also have high brightness of xenon lamp, so can say: a xenon lamp is a kind of headlamps.
Fog lamps, generally before and after, smaller than headlamps, mostly yellow.
This kind of light in the fog day, rainy day, and the line of sight is bad, open the use.
Fog lamps light penetration ability is strong, can make the line of sight of driving with a bit clearer, and at the same time also make before and after the vehicles and pedestrians more attention to the local situation.