No, catapults and trebuchet are arguably not the same thing. I suppose it depends on your definition of a catapult. If you define a catapult as anything that is used to propel a projectile in a given distance, then a ballista is a catapult.
To me, a catapult typically works based on a rope that is wound around a system of cogs; whereas a trebuchet works because of gravity and momentum.
They're different.
If you define a catapult as anything that is used to propel a projectile in a given distance
By that definition, most ranged weapons are catapults. Hands (rock throwing), bows and crossbows, slingshots, firearms, artillery, railguns, etc. etc.
The trebuchet, aside from using a different mechanism, also throws its ammo differently. While the catapult is like an oversized human arm, the trebuchet is like an oversized human arm using a slingshot.