The Queen of the United Kingdom is the head of state of many former Commonwealth countries
She is also the head of the State of Canada and Australia as well. Do you think she runs those countries as well?
It is mainly ceremonial, the Queen doesn't run these countries. Hell she doesn't run the UK. Boris Johnson, the Prime Minister, is the head of government in the UK.
The thing is that in America head of state is also the head of government, the President. So Americans get confused. It doesn't work like that is every other country