What creates the potential difference in a car battery

Apparently a battery is just a pump that pumps electrons through a wire and through itself. Well why are the electrons moving in the first place.

Well... technically, electrons are always moving. A current does not flow until there is a net movement of electrons in one direction.

As far as what "powers" the net movement... it depends on what type of car you're talking about, or more specifically, what type of battery you are talking about. For the standard lead acid battery, the driving force is the chemical potential of the corrosion of lead in sulfuric acid. When you use the battery, the lead is corroding. When you are recharging the battery, you are electroplating Pb back onto the plates.