Lets get some terminology straightened out here:
Based on several (won't say how many) years of experience, the common
use definition of various types of lights on motor vehicles would
probably go something like this.
Headlights:  Generic, for the front of the vehicle, can contain 'high'
beam, 'low' beam, or both.  Low beams set to illuminate immediately in
front and to the right of the vehicle.  High beams set to reach out
further in front of and to the right of the vehicle, but still not into
the path of oncoming vehicles.
Fog Lights:  Front or rear, often yellow in color, set low and aimed
parallel to the ground or slightly down to get under the fog.  Rear
mounted fog lights to make vehicle visible to vehicles behind.
Driving Lights:  Front of vehicle, mounted just about anywhere, usually
very bright, intended for off road or back road use and aimed way ahead
of the vehicle for maximum illumination at distance. Also used for high
speed driving at night to reach out further than standard headlight high
beams and minimize the chance of 'overriding your lights'.  NEVER TO BE
USED IN THE CITY OR WHEN THERE IS ONCOMING TRAFFIC!
Just because they are called 'driving lights' does not mean that they
should 'be on when driving'. So called 'driving lights' should at the
minimum be switched with the high beam headlights, and in most cases are
set up on their own switch and only used when needed.