Leadership and management are related to one another, but are not really the same thing.
Both leaders and managers in a business are trying to accomplish the same basic goal. Both are trying to get the business to succeed. Both have to do so, at least in part, by getting other people to do what they (the leaders/managers) want.
But leadership and management are also different. Leadership is about working with people and getting them to act in certain ways. A leader is trying to motivate his or her subordinates to act in ways that will help to achieve the firm's goals.
By contrast, management is about more than people. Managers do not work only with people. Instead, they work with machines and raw materials and processes. They do have to get their subordinates to act in proper ways, but they also have to do things like setting up the most efficient procedures in a factory or making sure that the right amounts of various inputs are being acquired at the right times.
In these ways, management and leadership overlap but are not exactly the same thing.