Usually in the 7 cities, the sheriff is an officer of the court, as opposed to a law enforcement officer. They carry out the orders of the court, similar to the way federal marshals operate (warrants, prisoner escorts and jailing, bailiff, etc.) while police officers are in charge of the day to day enforcement fo laws within the boundaries of the city and investigation of crimes (like the intoduction to "Law & Order).
Outside of this area, though, sheriff's deputies can take over all law enforcement duties, depending on the state/local laws.