Early Roman ballista were constructed mainly of wood which is liable to snap under extreme load. Although later examples were constructed of metal making them stronger and lighter. Also the torsion element of the weapon used animal sinew which was affected by the weather. Finally the ballista lacked the strength to throw very heavy missiles.
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The Romans created the first ballista. It looked like a very large cross bow. It throws things a long way (relatively). A ballistic missile throws itself. An anti-ballistic missile throws itself at the incoming ballistic missile.
A catapult was used as a weapon of seige. In other words a catapult was used to launch object into a city on at its walls. In one case catapults launched plague victims into a bedeiged city to poison the residents. The more common usage was to launch boulders at city walls to destroy them.