Arrest Warrant: Ordinarily, the police are supposed to obtain an arrest warrant, issued by a judge based on probable cause, before taking an individual into custody. There are, however, exceptions to this general rule that allow police to conduct warrant less arrests.
Bench Warrant: A judge issues a bench warrant when an individual fails to appear in court. It is not at the request of the police. It is based on the court's jurisdiction over individuals to require their appearance in court.