Leader---A leader moves forward, showing others the way. They don't take charge; others follow because they have faith the leader knows where they should go. This is a big picture person, they see things others don't or can't see. A leader is not afraid to take risks and chances because they know this is the only way to continue to move forward. They may motivate and encourage others, but their main goal is movement towards their desired outcome. The day to day operations don't matter as much to them as long as these activities aren't holding them back.
Manager---A manager focuses on the day to day activities and makes sure the people are doing what they should. Managers schedule and grade and are more concerned with what is happening now. Good managers will also coach and motivate, but see this as a way to get the work of today done in a better way. Managers focus on making sure things are running as smoothly as possible and will often be the ones tapped to make tweaks and changes to the operations in hopes to improve them. People don't follow managers, but in many cases, will respect them as the authority in their day to day interactions.
In almost all situations, it isn't possible to be both a leader and a manger at the same time. Yes, both of these positions are important, but they take different mindsets to accomplish. Great companies have both, but the world is full of managers, while leaders are much more scarce. All of us are capable of doing either...both take work, but leading is much more difficult than managing. Leading takes more time, a lot more courage and the ability to focus on where we should go. The world needs more leaders...where do you want to take us?