I would say that a C-claw is a grabber, hand, or clamp like mechanism with 2 jaws. Specifically, it grabs onto the cross sectional tube of the game pieces. It would not grip/adhere to it with rollers or scoop it and press on the top and bottom faces of a game piece that is lying on the floor ("pizza platter").
I would say this is a clear C-claw:
http://www.chiefdelphi.com/media/photos/36495
Debatable, but yes (has only one moving jaw, correct?):
http://www.chiefdelphi.com/media/photos/36531
No (roller):
http://www.chiefdelphi.com/media/photos/36542