This is the later model of the piccolo throw off, with a longer tapered "finger" that gave the drummer a bit more leverage than the original square one. As it came in roughly around the ubiquity of the standard "Orion" throw-off, I'm calling it the "Orion Piccolo Throw-Off".  And because the "long-finger" throw-off sounds somehow inappropriate!

There's no butt-end adjustment with the piccolo throw-offs.