I think GiftWraps are more like individual Tor messages that can include DMs inside them. 

They have the "next node" address that is visible (a pubkey which can be the real one, an alias or a new key every time), but everything else is either random or encrypted. 

The GiftWrap event can encrypt other GiftWrap events that together assemble be a full onion route with the benefit being that the final node is the client, not the relay. It would be like never hiting an exit node in Tor.

But we are on early days. I am still wanting for a real cryptographer to make sure our thinking doesnt have any holes in it.