A leader can be a manager, but does not need to be a manager. You can lead/be a leader without being a manager.
An example that I have heard used often is that the leader will climb the ladder, the manager will make sure we have the ladder, it is stable and it is against the right building. Leading has more to do with the vision and taking the people with you. Management includes leading, but also covers the how and other similar things. (PS I think the original ladder example might be from Covey. Have a look at his stuff on leadership v managers)