Coaching
Coaching is a form of development in which a person called a coach supports a learner or client in achieving a specific personal or professional goal by providing training and guidance. The learner is sometimes called a coachee. Occasionally, coaching may mean an informal relationship between two people, of whom one has more experience and expertise than the other and offers advice and guidance as the latter learns; but coaching differs from mentoring in focusing on specific tasks or objectives, as opposed to more general goals or overall development.
Management
Management (or managing) is the administration of an organization, whether it is a business, a not-for-profit organization, or government body. Management includes the activities of setting the strategy of an organization and coordinating the efforts of its employees (or of volunteers) to accomplish its objectives through the application of available resources, such as financial, natural, technological, and human resources. The term "management" may also refer to those people who manage an organization.
Management
You manage things, you lead people. We went overboard on management and forgot about leadership. It might help if we ran the MBAs out of Washington.
Grace Hopper (1987), quoted in "The Wit and Wisdom of Grace Hopper" by Philip Schieber, OCLC Newsletter, No. 167 (March/April 1987)