I'm pretty sure education administration refers to secretarial & authority roles in an institution or school, and educational management is a role in management of grounds, security and repairs, etc.
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the link between strategic management and leadership
Both are the same I think management institute also concern with the leadership also .you can Google the best ILM training organization for this.
answer
Leadership is the ability to influence others through inspiration and motivation, and Management is the ability to control people and resources using authority to achieve specific business objectives. From MoCreaTV youtube channel.
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Leadership is setting where we are going, while strategic management is smartly overseeing the critical issues of how we get there.