You're welcome! I also always got confused on this issue.

I had actually tried to come up with some better names. Below are my notes from trying to come up with terms. I think the term I found on that forum post, of Delegated Custody, is much better than what I came up with.

hosted wallet (positive spin) on "not your keys" controlled wallet - negative spin custodian controlled wallet external-control wallet external-custody wallet vs self-custody wallet