What is a capital of state?

A capital of state is the country's capital (countries are sometimes referred to as 'states') except in the case of the USA where 'states' is the name used for 'counties', 'sectors' or 'provinces' and they each have a 'capital of state'. In that case the 'capital of state' is just the capital city of that province or county not the county for the country. For example:-
State(county)-Washington D.C.// Capital of State-Olympia