Whats the difference between a Sheriff and a Police officer and State Trooper?

They are all sworn officers with arrest authority but besides the varied work they do it boils down to jurisdiction. City officers have jurisdiction within the city limits. Sheriff Deputies have jurisdiction within the county limits and state officers or troopers have jurisdiction anywhere in the state. Now do we see State police doing traffic stops inside the city limits very often no as they focus on the interstates and highways while the Sheriff's deputies are concerned with the county and do the majority of serving subpoena's as well as run the local county jail while the municipal officers concern themselves within the city limits like you would see more often every day if you live within a city or town.