Actually, the use of the verb drive in each sentence is correct.
In the first one, drive acts like a transitive verb with the direct object being car.
In the second one, the verb drive is intransitive denoting an action that involves the operation of a vehicle -- or any other object for that matter.
Consider the game of golf in which one player is unable to drive the ball because of a shoulder injury. So, he has a substitute doing the driving for him while he is able to do the putting for himself.
Any more information that is needed I will gladly supply. I am driven to help you.