The term “drive” refers to driving horses, mules or oxen. Drive meaning to push forward the animal. In the days of a horse-drawn carriage, the driver would be in charge of the vehicle. A car is a horseless carriage and so borrowed from the horse terminology.
The term “pilot” means to guide direction. We had pilots prior to air travel, for example, a boat or ship may have a pilot. A ship pilot is in charge of plotting the course and navigation decisions. A ship coming into a harbor will take on a harbor pilot to guide the ship into port.
Since aircraft were never hitched up to a horse, it would have been odd to use the word “driver” to refer to the operator. An aircraft pilot does do the job of navigating. In addition, the first aircraft were not fixed wing planes, but balloons and airships. The airship crews borrowed much of their terminology and methods of operation from ships.
In some early media, aircraft crews are referred to a “aeronauts” in a similar way as we today talk about astronauts in space. The word “aeronautic” is still commonly used to refer to things related to flight.
Thus we drive a car, truck, carriage or herd of animals but we pilot a plane, boat, ship or spacecraft.