Anyone who's ever studied it knows that there's nothing logical about language!
What is "right" and "correct" is nothing more than what common usage is among people in a given time and place, as previously mentioned.
The Frence use the word "Mangonon" to describe the HCW type of trebuchet. "Trebuchet" being the word for the FCW type. In England, "Catapult" is what we yanks would call a slingshot (but don't call anyone from the deep south a "yank", or you'll probably end up in a heated argument!...)
"Mangonel" is derived from a word the Greeks used for any engine-type military weapon. It means "engine of war". The Greeks invented both the Ballista and the single-arm torsion type machine, which was later made popular by the Romans.
The Romans took the single-arm torsion machine, and make it bigger and stronger. They called it a Scorpion at first, because the arm and hook resemble the tail and stinger of a scorpion. Also, it "stings" the enemy... Later they started calling it the Onager, which is a type of donkey, becuase the back end of the machine "kicks" up like a donkey. The Onager (donkey) also has been known to kick-up rocks as it runs away from an attacker.
So, in the US and England (but not France), Onager and Mangonel are essentially the same machines. In England you're more likely to hear "Mangonel", in the US "Onager" is the more popular term.
If you want to take on a more Greek influence (they invented the damn things after all!) use "Mangonel". If you want to be Roman (they used the machines to the best advantage) then call it an "Onager."
--Ron