a track car is usually a street car prepared for the track. can also be towed, but it is usually just a track toy meant for playing around.

a race car is...well, a race car. full current spec FIA approved car. Everything including up to date seatbelts, seats, cage, fire supression system, etc etc. On track cars many people will buy older seatbelts for cheap, but they "expire" after a certain amount of time if the car is going to be scrutinized for racing.