Leadership and management are abilities that are far too often confused and conflated in mainstream discourse. There are some similarities between the two, but they are in fact very distinct abilities that encompass a different set of skills and qualities. Good or great managers are present in many organizations while good or great leaders are much scarcer. The skills needed to be a great manager can be developed and honed while the skills necessary to be a great leader tend to be more innate and more difficult to learn (although not impossible).
Managers can manage any number of things. They can manage a task, subordinates, projects, transitions, meetings, or even expectations. Leaders lead people. That is the essence of the difference. A great leader must have the ability to inspire and compel followers (subordinates in the case of a company) to act and perform on behalf of something that may or may not serve their own self interest.