Although the Holy See is closely associated with the State of the City of the Vatican, the independent, sovereign state governed by the Holy See, the two entities are in fact separate and distinct. The Holy See administers the Vatican City, including all diplomatic functions; foreign embassies are accredited to the Holy See rather than to the Vatican City, and the Holy See establishes diplomatic agreements ("Concordats") with other sovereign states, on behalf both of itself and of the Vatican City (as appropriate). Generally speaking, the Holy See is a party on its own behalf to treaties of Ecclesiastical interest, and a party on the Vatican City's behalf to treaties of technical significance (e.g., regarding co-operation with Italy).
Because the Holy See comprises more than simply the Pontificate, it does not dissolve upon the death of the reigning Pope; in contrast, the heads of the dicasteries of the Roman Curia (such as the prefects of congregations) cease to hold office immediately upon the Pope's death. During a Sede Vacante -- i.e., the interregnum occurring between the Pope's death and the election of his successor -- the government of the Holy See (and therefore of the Catholic Church) falls to the Chamberlain of the Holy Roman Church, the prelate appointed by the Pope to administer the temporalities (i.e., properties and finances) of the Holy See; canon law prohibits the Cardinal Chamberlain from introducing any innovations or novelties in the government of the Church during this period.
The Holy See is also called the "Apostolic See", although this name properly refers to any of five sees founded by an Apostle; the five Apostolic Sees, all of which are of patriarchal rank are (in descending order of precedence): Rome (Ss. Peter and Paul), Constantinople (St. Andrew), Antioch (St. Peter), Alexandria (St. Mark), and Jerusalem (St. James the Greater). Aside from Rome, the archiepiscopal See of Mainz, which was also of electoral and primatial rank, is the only other see referred to as the "Holy See", although this usage is rather less common.