[JackCh]

IANAL but as I understand it, the circumstances under which a 'private citizen' is permitted to arrest people are more restrictive than the circumstances under which a police officer is allowed to arrest people. Namely that a 'private citizen' is only allowed to arrest people for crimes that are committed in the presence of the person performing the arrest, whereas police are allowed to arrest people for crimes that were not committed in their presence.

(Police officers are (almost?) always citizens, despite that term sometimes being used in a way that excludes police)