“Hes talking about the origin of the Vatican state, not the origin of the Catholic church.”
Same thing.
“Same thing.”
No, not at all. We don’t send ambassadors to churches.
Vatican City/State is a diplomatic and political site which, for the time being, houses some of the administrative offices of the Catholic Church. The Catholic Church itself is much vaster: it extends across around the world, and from Pentecost until Christ comes again.
Thus, the Vatican state and the Catholic Church can be distinuished. See here (Link)