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.
Planning is the process of thinking about the activities required to achieve a desired goal. It involves the creation and maintenance of a plan, such as psychological aspects that require conceptual skills. There are even a couple of tests to measure someone’s capability of planning well. As such, planning is a fundamental property of intelligent behavior. An important further meaning, often just called "planning" is the legal context of permitted building developments.
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)