Sheriff's have unique powers. They can convey arrest authority i.e, deputize just about anyone they want, so a posse member could conceivably have arrest powers if the sheriff so chooses. As was stated before many sheriff and police departments have reserves. Typically unsworn but they can wear uniforms and carry guns. Often used for parades, traffic control, security details, concerts etc,etc. Some are allowed to ride along with regular officers. When working with a sworn officer they pick up the same arrest authority. In many states in order to have arrest authority you have to go through a training academy but the county sheriff has unique powers. Bottom line is that a sheriff posse could have arrest authority or could just be reserves.