A pulley is a wheel which is driven by a power source. Connected to the wheel is a belt which in turn is connected to another wheel. When the wheel which is connected to the power source turns the belt drives the second wheel.
With a gear system the wheels are in direct contact and each has teeth round its edge. The teeth from one wheel drive the teeth on the other wheel which in turn makes the wheel go round.
In each of these cases one of the wheels is the driver ( the one connected to the power source, usually a motor) and the other wheel is the driven. It is not necessary to draw the wheels just as they look, instead we represent the different types by drawing circles like the examples below.

Gear System

Changing the direction of motion.

With a pulley system this is easy all you have to do is make the belt in a figure of eight. This makes the wheel which is being driven turn in the opposite direction to the driver wheel.

With gear wheels the method is different. You have to add a third cog which is called an idler. This does not have any effect other than to change the direction of motion.
All the examples shown so far have illustrated wheels in a flat formation and all of them rotate. If the motion needs to be changed through 90 degrees the types of gear wheel need to be changed. If the motion needs to be changed from rotary (round and round) to linear (backwards and forwards) then different types of gears are needed.