A sheriff is responsible for law enforcement in a county, while a police officer is responsible for law enforcement in a specific town or city. The duties of a sheriff include investigating crimes, arresting criminals, and responding to emergencies within their county. On the other hand, a police officer maintains law and order within their city limits, and also arrests individuals, investigates crimes, and responds to emergency situations. The key difference between the two roles is the jurisdiction, with a sheriff covering an entire county and a police officer covering a specific town or city.