Peter was the head of the universal Church; James was the head of the local church in Jerusalem, in union with Peter. Although Peter may have taken responsibility for a local church, as he did eventually in Rome, his primary responsibility was head of the universal Church. The same holds true today: The pope is the head of the universal Church and bishop of the local church in Rome. Other bishops are heads of the local churches to which they have been appointed, in union with the successor of Peter.
