The words originate from BattleTech and the western release of Robotech.

Often mistook for Japanese name for the large robots, but the Japanese word meka (メカ) comes from English word mechanical, which includes toasters, cars and anything else exactly that, mechanical.

Mechs are practically (somewhat) humanoid shaped bipedal walkers of unspecified size though they must be a lot larger than humans so they don't get categorized as power armor. Or other large vehicles (piloted robots) that usually have at least arms or arm-like extensions and/or legs.

If the user must move with the mech to accommodate its movements, it's a power armor. If the user is in actual cockpit, it's a mecha.
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