The Holy See is not the Vatican
The truth is that the Catholic Church has a unique status in the world because of its religious and political influence. The Pope, who is the head of the Catholic Church, is both a political and religious leader. He is the head of both the Vatican City and the Holy See.
While the Vatican City and Holy See are often mistakenly used interchangeably, the two are distinct. The Vatican City is a city-state, meaning that it is a distinct geographical entity and the world’s smallest country by population and size, with the Pope as the head of state. However, Holy See is not a geographic region or country, but a sovereign entity and the jurisdiction of the Pope. It is the central governing body of the worldwide Catholic Church, headquartered in Vatican City. So, Vatican City is used when referring to a country while Holy See is used when referring to the area governed by the Bishop of Rome, which includes the Vatican and the entire Catholic Church.