The superintendent of schools of a unified school district that is coterminous with the boundaries of a city and county shall have all the powers and duties set forth in this code for a superintendent of any school district of the class of school that is included within the unified school district and also shall perform the duties of the county superintendent. The superintendent shall have his or her compensation fixed and ordered paid by the board of education, anything in a city, county, or city and county charter to the contrary notwithstanding.