Toureman, I think that will make a difference only if you are speaking to someone from a country where they drive differently (apart from the small number of left-hand-drive cars in this country), so in practice there is unlikely to be confusion. Every Brit knows which side the driver's side is. So does every American.
Nearside and offside are terms most well known by the motor trade. They are terms that VOSA use to describe which side of a car is meant in the MOT test.
Left side and right side were not acceptable terms by VOSA when the MOT fails were handwritten.