In general (and historical) usage, ballistae and catapults are two different families of war machine.

Ballistae are ballistic weapons, like cannons, guns, crossbows & bow. They can fire both directly and indirectly but they are most effective when using direct fire.

Catapults are not ballistic weapons, their most effective mode of fire (and in most cases their only mode of fire) is indirect fire, like a modern mortar.

Trebuchets are one type of catapult, but neither trebuchets nor catapults are ballistae.

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