Leading and managing are two different things...yes. Leading is quite a challenge, however. Versus managing, leading has more to do with how the team functions from the inside out. Managing however, has to do with how the team functions overall. See the difference? Let me explain...
You see leaders are all about leading people to a certain point. It requires progress from start to finish. Management is more like managing progress. When you're a leader, you're required to get people to a certain point. Management, there are no specific requirements.