Leadership is strategic while management is tactical. Leadership involves setting the vision, strategy, motivating and aligning people and resources to deliver on them. Management is about dealing with the complexity of tactical tasks to deliver on initiatives in a repeatable predictable manner. Management plans, budgets, solves issues.
Successful leaders are required to balance both traits while managing organizations. It is not an either or situation.
Here is a good HBR piece that explains both Management and Leadership.