yes, what I call groups are definitely islands in your case. edge selection was lost a few times trying to get a result with no succes but what you show definitely sounds like a good start.
got the AutoUV window open, my faces painted and my edges selected.. how do I "get the islands"? nothing shows in my AutoUV window
got the AutoUV window open, my faces painted and my edges selected.. how do I "get the islands"? nothing shows in my AutoUV window