Someone with more intimate knowledge of OpenID can feel free to explain the technical names for these things.
I have spent the last two weeks implementing it at my day job and I still can't keep the names straight. OpenID is like a case study in obtuse nomenclature.
Let'se see: the first URL isn't a URL. It is an Identifier. To be specific, it is a User-Supplied Identifier. It isn't a Claimed Identifier, you see, because that would uniquely represent the user. You perform Discovery on the User-Supplied Identifier to determine what the Endpoint is to redirect the client to so that the OP can assist the user in moving from a User-Supplied Identifier or possibly an OP-Local Identifier to a Claimed Identifier.
I think I have that right. I'm not sure -- I only implemented it.
True story: I was at an OpenID developer meeting some time ago and BradFitz was asking people to explain all this crazy nomenclature, because even he can't quite follow it any more.
OpenID is a simple idea that was seized upon and overwhelmed by a large number of asshats who wanted to embrace and extend the concept with dopey shit like XRIs.
Unfortunately, those people have way too much influence on the written spec. This is not to denigrate anything daveman692 is doing and BradFitz did, it's the other people that I wish would fall off a cliff.
Isn't the single URL approach more user (& developer) friendly, though? It allows developers to just put in a "sign in via Google" button, instead of confusing users by requiring them to enter their OpenID URL.
