This a good question! Leaders differ from managers in a few critical ways. The first way is that leaders have a vision for the direction of an organization, while managers are charged with implementing the vision. Leaders have a vested interest in the vision and make the necessary sacrifices to bring the vision into reality, while managers are invested in the vision only to the extent that the vision set by the leaders requires a minimum sacrifice.
Managers are by nature technicians, and leaders are by nature architects. The differing roles do not diminish the importance of managers; leaders need managers to organize, structure, and implement a vision. Leaders think in broad terms, and, without the organizational skills of good managers, they have no way to transform their vision into action.
Differences between the two can also be observed in the people who work for and with leaders and managers. Those who work with leaders volunteer and submit to the vision of the leader willingly. Managers have workers who answer to the manager because of a financial interest (such as their pay), or because, in the hierarchy of the organization, they are under the direction of the manager to implement a process. People who work with leaders are willing to give up something in return for being part of the team, or they derive an intrinsic benefit from being part of the vision. Those who directly report to a manager are not as interested in the vision as they are in the extrinsic benefits of being part of the team.
It is important to note that, though we don't think of managers as leaders, they are--in their own right--leaders to the extent they have a role in moving the organization in the direction of the leader's vision. However, it would not be inaccurate to say that many a vision has been undermined when the support of the manager is less than enthusiastic. Leaders must choose who they work with very wisely if they are to be successful.