What is the difference between a driver pulley and a driven pulley?

Hint: Pulley is a simple mechanical tool used to make the task easy by reducing the effort to do some work. The Pulley system is used in lifting heavy objects because of this they are used in cranes and other such machines.

Complete answer:
When two pulleys are connected through a belt and driven by a motor, the pulley which is connected to a motor is known as the driving pulley since the second pulley is driving by first because of the belt connected to a motor setup as shown in the figure below.

From this, we can conclude that the pulley which is connected to a motor is responsible for the source of mechanical power and drives the entire setup.
Hence pulley that connects to the motor is termed as the driving pulley and the pulley which is connected to a belt and driven by moving belt drive is termed as the driven pulley.

Additional information:
When two pulleys are connected and driven through a belt, such setup is generally termed as belt drive and they are further classified as
1. Open belt drive: In this set up both pulleys are directly connected as shown below and both pulleys rotate in the same direction

2. Crossed belt drive: In this set up both pulleys are connected with a crossed belt setup as shown below and the direction of rotation for both pulleys are in opposite directions.

Note:
We must note that this kind of setup is also applicable for gears. Also, the final speed of the driven pulley will depend on its size, and for maximum output, the driven pulley is generally bigger compared to the driving pulley. This concept is used in the gearbox of motor vehicles as well to increase or decrease the speed of vehicles.