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.
Animesh Chakraborty (born June 30, 1935) is a Bengali Indian academic and a professor of chemistry In 1975, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in chemistry by the Council of Scientific and Industrial ResearchAfter his graduation from the Scottish Church College, he did his postgraduation from the University of CalcuttaHe had subsequently earned a doctorate in chemistry from the University of CalcuttaHe had started as a research associate at the MIT and Harvard He had also served as professor and head of the department of chemistry at the Indian Institute of Technology Kanpur, and as professor and head of the department of inorganic chemistry at the Indian Association for the Cultivation of Science at the University of Calcutta, and as a visiting professor at the Texas A&M University He was also the Hindustan Lever Research Professor at the Jawaharlal Nehru Centre for Advanced Scientific Research He had guided fifty eight PhDs and numerous postdoctoral associates, many of the former students have become well known personalities and are doing outstanding work in academic and industrial organizations in India and abroad