I recall a woodwork/metalwork teacher at school giving an explanation for this. I don't there's any real reason behind the Americans using the letter "C" and the English using the letter "G". After all, it looks like a "C" without the screw, but a "G" with the screw. I think it's just the way the names evolved. But my teacher's explanation centred around how the device was used. Apparently, if the device is portable it's a cramp, but if it's designed for securing work to a single machine, bench etc. it's a clamp. That's what he told us anyway.
Chris