Constitutionally a cop is just a civilian that has arrest power (as all citizens do according to common law), whose full time job is to arrest people that break the law. As opposed to a regular citizen that can voluntarily arrest someone, but is not required by law to.
Of course they've built up a bunch of unconstitutional laws around them making them immune to criminal prosecution and immune to civil prosecution.
Personally I think we need to go back to elected Sheriffs and deputies.