"Theocrat" indeed seems to be used with that meaning too. But I understand that it has a more extreme meaning: a theocrat wants the government to be exercised by priests, or officially submitted to some church. Or is a member of such a government.
The Taliban and the Revolutionary Guard in Iran are theocratic. But the Catholics who made divorce illegal in some Catholic-majority countries are not generally "theocrats" - they don't want gov by priests or the Church.