A differential serves the following purposes:
It aims the motor power at the wheels.
It acts as the final gear reduction in the car.
It transmits the motor power to the wheels while allowing them to rotate at different speeds.
Why should we allow the wheels to rotate at different speeds? This is because the wheels actually spin at different speeds when turning.
The main drive shaft has a gear which interacts with the diff unit. This gear is also called a pinion gear. The large gear of the diff unit that it interacts with is called a ring gear.
The small gears inside the diff unit are commonly being referred to as spider gears. The spider gears that hold the shaft cup’s shaft is also called the side gears.
This third party video is not RC specific but is VERY informative regarding differentials:
