The Holy See is a jurisdiction rather than a country, and international law has treated it as a sovereign subject on that basis. It signs treaties, receives and sends ambassadors, joins international organisations and maintains diplomatic relations with the great majority of the world's states, and it did all of those things during the period between 1870 and 1929 when it held no territory whatever.
Vatican City is a separate thing, a small state created in 1929 so that the See would have ground it could not be deprived of, and the two are frequently confused in ordinary usage. The clearest demonstration that the See is the office and not the place is what happens when a pope dies or resigns. The See does not lapse; it is described as vacant, its ordinary business is suspended, a limited administration continues under fixed rules, and the diplomatic relations remain in being until a successor is elected.
Eamon Duffy's history of the papacy follows how an episcopal see acquired that standing over many centuries, and how contested it was at every stage. For the atlas the distinction matters practically, because a great deal of what is popularly attributed to the Vatican is properly an act of the Holy See, and the two have different legal identities.