I concur that they might operate differently based on the difference in names.

The names come out of the AoL, from those who made the things in the first place. There is a clear distinction between ter'angreal and the others in function and operation. The name separation between sa'angreal and angreal implies some fundamental difference between the two classes beyond mere sizing.

Don't forget that Jordan had a trained and educated military background and in the military differentiation between guns, rifles, howitzers and cannons are based on function, not size. A sixteen inch weapon can be a rifle (if the barrel is rifled for spin), a cannon if not, a mortar depending on barrel length and so forth. The same applies to naval ship classes, function is the primary differentiation.

Separation of the classes based merely on size seems too simplistic, although I will accept correction if proof is found. I don't claim to know what the difference is, merely that one is likely to exist.

Also, challenging the idea that Asmo and Rand drew the same amount from the CK because they were tired. How astronomical would the chances have to be for both to end up at an identical starting strength that was multiplied by the CK. It makes more sense for the CK to give access, in equal amounts, to a fixed amount of the Power. Occam's razor and all that...