Usually, a race involves people getting from one place to another. Running is a kind of racing where people try to be the first person to run from the where the race started to the goal or finish line. People also race in cars, boats, airplanes and other vehicles, and on animals like horses. Animals and machines can also race without people riding them. Often they race on a race track.
Some contests are not races. They could involve contestants trying to get the highest score in a particular quiz.