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.