I've always considered (and consistently heard of) a half-volley to be a pickup directly off the bounce, with a shortened swing than one would normally employ on a groundstroke.
I have never heard of it used with respect to a specific volley technique/stroke.
Plus, wouldn't what you describe as a "lengthened" volley be too similar to a regular volley, save the firmness of the shot?
EDIT: Some first videos that come up when searching for "half volley"
http://www.youtube.com/watch?feature...zQCZmzI#t=116s
http://www.youtube.com/watch?v=cZ3nrVfNTOU