Cat's Claw/Gou Teng confusion

I've been slowly implementing my core Buhner protocol over the last several months - and have the most recent book. Despite reading about the various Uncarias, I'm still a bit confused. I do understand that use of both U.tomentosa and U.rhyncophylla are preferred in the protocol.

I've seen mentioned "Chinese Cat's Claw" and Cat's Claw, and believe them to be the same?
Then there's Gou Teng... which is U.rhyncophylla?.... so Gou Teng is Cat's Claw also? If so, why does it have it's own name? Also, I purchased a shredded Gou Teng bark called "Gambir" and was hoping to make a tincture. Is that NOT U.rhyncophylla? Still sorting through the most economical way to consume all of these great herbs. Thanks all!