Catapults all have one purpose: to hurl objects, or projectiles, into the air. These projectiles can range from the harmless ping-pong balls launched in a classroom to huge stones meant to crush enemies. Though most people imagine the catapult to be a contraption that looks like this, ” 
“, there are actually three types of catapults.
1. The catapult is the winched-down bucket that people generally think of when the word “catapult” is said. These catapults were large weapons invented in the Middle Ages, normally on wheels, with a basket attached to a long wooden arm and a power source for hurling objects into the air. The power source normally comes from the gears, which can apply to all the catapults listed (more on that later)
Picture of catapult: 
2. The ballista is a large crossbow, and it’s “ancestor” was actually the first version of the catapult. It’s “ancestor”, the Gastraphete, was invented in 400 BCE in Greece. The Greeks were apparently so impressed by the mass destruction of the Gastraphete that they invented a bigger version, which is known as the ballista.
Picture of Ballista: 
3. The trebuchet is a weighted beam that swings a sling carrying the projectile. It is the most recent creation of the catapult family. The trebuchet, unlike the catapult or the ballista, uses the principle of a counterbalancing weight. In other words a heavy weight is fastened to one end of a large beam and a pouch for the projectile on the other end. The beam is on a solid stand or a supporting frame, and is able to launch the projectile in the pouch rather far.
Picture of trebuchet: 
Gears are very important because they create winches. Winches allow people to put a great amount of energy into a catapult over time, and when all the energy is released, the projectile is launched.
Those are the three main examples of a catapult.
Sources:
http://science.howstuffworks.com/transport/engines-equipment/question127.htm
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