Leadership is a choice. It's not a rank, it's a choice. I know many people who are at the top of their organization who have authority. We have to do what they say because they have authority over us. But they're not leaders. We wouldn't follow them. They may be at the top of the company but they're not leaders.
Leading is not the same as being the leader. Being the leader means you hold the highest rank, either by earning it, good fortune or navigating internal politics. Leading, however, means that others willingly follow you—not because they have to, not because they are paid to, but because they want to.