Fog Lights

Fog is composed of tiny droplets of water suspended in the air. Fog lights are aimed lower so they do not reflect light off of the suspended particles into the driver's eyes. Fog lights may be colored white or yellow and typically illuminate the road 20 to 30 meters.

Low-Beam Lights

Low-beam lights are designed to allow driving visibility without shining in the eyes of oncoming drivers. Low-beam lights produce wider and lower beams than high beams.

High-Beam Lights

High-beam lights allow drivers to see farther than low beam lights but will blind drivers of oncoming vehicles.

Driving Lights

Driving lights are sometimes installed as aftermarket lights and they differ from high-beam lights. Driving lights project a narrower, higher beam and are designed to allow drivers to see 200 to 500 meters and farther. Driving lights are sometimes called off-road lights.

Laws

Some states do not allow the use of fog lights except in foggy conditions. Driving and high-beam lights should not be used in the presence of oncoming traffic. Additionally, some localities do not allow more than two sets of headlights operating simultaneously (low beams and fog lights, for example), and some localities limit it to one set. Check your country and state laws if you are unsure.

Source:

RiotAct: Fog Lights and Driving Lights

AutoAnything: What's the Difference Between Driving Lights and Fog Lights?