Canonical is based on the board URL set in the control panel. Full is based on the actual URL being accessed, which might not be the same thing (though generally is).
So "full" is the actual URL, but "canonical" is the URL you want to advertise? That means a canonical URL could have a redirect in it, but a full wont?
As an example, assume we didn't have any redirects in place and I accessed this forum via http://www.xenforo.com/community/ (regular HTTP and with the www). Then this: