The word driver is more general - anybody who drives a vehicle is a driver. You are a driver when you are driving your car. Some people work as bus drivers and taxi drivers (the drivers of trains are usually called conductors).
A chauffeur is a person who is employed to drive a car for a private individual. Rich people and celebrities often have chauffeurs so that they do not have to take public transportation, or drive themselves.
All chauffeurs are also drivers; not all drivers are chauffeurs.
Fact
Roger Bannister of Great Britain was the first man to run a mile in under four minutes. On May 6, 1954, he ran the mile in 3 minutes 59.4 seconds. .. More >>