I think the change to the key system makes it clearer, especially on the developer-side.
Anyway, those keys are likely the keys you used to get the game on Desura.
I havent yet looked first hand, but from the "invite" side of things it sounds like social marketing - though getting your key again - are they looking at trades maybe?
Desura keeps track of who redeems what key and, as you probably know, will even show you the account who redeemed a key if you try to activate a used one.
"Invite" is the default Desura key category under the old system. There were also"Prize", "Press", and "Tester" categories and for those keys, they show those names instead of "Invite".
You're just seeing the list of keys you've already redeemed and the wording is a little strange, but that's carried over from the old system, which I found to be a bit confusing.
Now, non-Desura keys are a different matter, you can use those depending on what key they are... Steam... GOG... etc. "Unlock keys" are for games that have a key to enter inside the game, say for multiplayer or something.