Management is doing things right; leadership is doing the right things. - Peter Drucker
Managers find what is unique within individuals within a group and use it to the group’s advantage. Leaders find what is common and universal and rally the group around it to achieve goals. Being a manager and leader is not mutually exclusive, but this distinction helps understand the roles and requirements of each1.
Change
John C. Maxwell frames leadership being about change, while management is about stability. A leader needs to lead others to a new place, a manager executes on a stable process2. While this does provide a pithy summation of the difference, it probably is not reflective of the reality of the modern manager. In Maxwell’s framing of a “manager” is a line boss who is just trying to execute the playbook and go home. He is not concerned with effecting change and growth within his reports. Meanwhile, a leader is looking to change and improve an organization (think executive). Most modern management philosophies would encourage growth, coaching, and feedback which are qualities Maxwell attributes to a leader. Regardless, it is important to think about leadership within the context of change and pursuit of a goal.