An official residence is a residence designated by an authority and assigned to an official, and may not always be the same place where the office holder conducts their official functions or lives.
Casa Rosada, Buenos Aires
The Government House, Yerevan
Government House, Melbourne
Hofburg Neue Burg section, seen from Heldenplatz.
A head of state is the public persona of a sovereign state. The specific naming of the head of state depends on the country's form of government and separation of powers; the head of state may be a ceremonial figurehead or concurrently the head of government and more.
Grassalkovich Palace in Bratislava is the seat of the President of Slovakia.
King Harald V of Norway
Charles de Gaulle, President and head of state of the French Fifth Republic (1959–1969)
George Washington, the first president of the United States, set the precedent for an executive head of state in republican systems of government