Managers and leaders have completely different ways of getting things done. That is not to say that one is better than the other, but there are distinct differences.
Managers have subordinates. They are largely task oriented and get things done simply because they are in charge. They have the authority to tell people what to do and have them do it. .
A leader has followers. They get things done because they make people want to do them. Their authority is granted to them by their followers. .
Managers can become leaders, and leaders can become managers. While you can teach someone to manage, leadership is by and large an inherent quality. While one can learn leadership skills, without the innate ability to compel people to follow them, they may fail in the leadership role, while excelling in the management role. .
While management is somewhat mechanical, leadership is always based on perception by others. This perception is what makes people want to follow and please their leaders. .
Leaders help us understand and make some kind of sense of our situation and environment. When things don't seem right, or are unclear, they are able to explain in language that we understand. Managers don't need understanding, they need compliance, and while they can help us along, it is in order to gain that compliance, not to reach understanding. .
Leaders help us see the direction in which we are heading. They make us believe in a brighter future, and convince us we can achieve our goals. Managers tell us where we are going, and give us a detailed map, then leave it to us to get there.
Leaders make us believe in important values. They make us feel like we are a part of something, not just a lone voice in the wilderness. Managers tell us that we are a part of something, but do nothing to foster individuality, instead looking for conformity.
Leaders make us feel powerful. They give us choices about how to live our lives.