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they cover rural areas that city cops can't get to.
Actually, in most places other than Hampton Roads, the sheriff is the only law enforcement official. It just happens that the 7 cities in this area are all independent cities and don't belong to a county and that's why the police patrol the city while the sheriff's office does the jail. In the areas that have a city police department as well as county sheriff's departments, the city police stay within the boundaries of that city while the county sheriff's office has jurisdiction over the whole county including the city.
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.