The Difference Between Vatican City and 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 the Vatican City.   The word ‘See’ derives from the Latin word Sedes meaning ‘seat’ referring to the episcopal chair that a Bishop occupies in the area overwhich he exercises his ministry. 

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.