It is important for a manager to be a leader. Leadership ability is not the only thing that a manager needs to have, but a person cannot be a top-class manager if they have no leadership ability.
Much of management has nothing to do with leadership. You do not have to be a leader to set up work schedules. You do not have to be a leader to watch your employees and determine who is doing well and who is not. You do not have to be a leader to set up procedures that can make the work place more efficient. All of these are things that managers should be able to do.
However, there is a leadership component to management. The best managers are those who can get their workers to give their best effort. The best managers keep workers satisfied with their jobs and with the way they are being supervised. Managers need to have leadership ability and knowledge in order to get the best out of their workers.
Thus, while management and leadership are not one and the same thing, leadership is an important aspect of management.