一般城市裏的警察叫police officer, county的警察叫deputy sheriff

deputy sheriff and sheriff's deputy interchangeable.

The main difference between a deputy sheriff and a police officer is their jurisdiction and the level of government they serve. Police officers are employed by municipalities (cities or towns) and enforce laws within those city limits, while deputy sheriffs work for county sheriff's offices and enforce laws throughout the county, including unincorporated areas and smaller towns.