First theory is theory by Peter Drucker and Second one is by the Henry Minzberg.
Peter drucker gave these elements: Setting objectives, Organizing work, Motivating and Communicating, Measuring and Developing people. And he gave three aspects to the responsibilities of Managers I.e, Managing the business, Managing managers and Managing workers.
Henry Minzberg introduced three management roles: Interpersonal, Informational and Decision making. Manager as a figurehead, as a leader, as a liaison, monitor, disseminator, spokesman, initiator, disturbance handler, resource allocator, and negotiator.