What are some differences between a trebuchet and a catapult?

a catapult a generic term for a siege machine that chucks things. a trebuchet is a type of catapult. there are big and small trebuchets. a ballista is also technically a type of catipult even though it is a big bow and arrow on wheels. kind of like a square is a rhombus but a rhombus is not a square.
a trebuchet uses a counter balance a folcrum and a ratcheting mechanism to chuck the projectile. other types of catipults use potential energy stored in twisted ropes, bent wood etc etc.
A trebuchet was a much more heavy and powerful version of a catapult. They both used the same technique for propulsion of the stones, but a catapult was smaller in size, easily portable, but had very less range. A trebuchet, on the other hand was huge, and had to be assembled at a site for it to be ready to use. After this assembly, it was not possible to move it. For that, it'd again have to be disassembled. And it had tremendous range, many times that of a catapult.
"Catapult" is a more general term, a trebuchet is one specific form of a catapult.
Link below has more information.
The other difference is that a catapult commonly had a solid throwing arm which hit a stop to launch the object. A trebuchet has a rope and pouch arrangement like the "David and Goliath" slingshot. The rock starts out below the swing arm, and ends up moving quite a bit faster than the end of the stick. Then the loop on the end of the rope comes off the hook, and away she goes. Fair photo of a small one here:

They are both medieval siege engine, and have the same purpose: to throw projectiles at your enemy, but they work on different principles. If you search on wikipedia you will see a significant difference in their design.
A catapult functions based on the principle of stored energy released with a winch, is smaller, mobile and has a shorter range.
A trebuchet is based on the sling principle, could deliver a greater payload of stones, iron or any other kind of projectiles, has a greater range than the catapult, but it was not mobile.

Check wikipedia for more information (especially the design differences).

Hope this helps you.

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