Managers are not necessarily leaders. Managers, by definition, constrain people to meet an expectation.
Leaders blaze new trails. They blow out expectations. They're out in front of others.
Setting a goal is not leadership. A leader may or may not set the goal, but they damn well recognize the right direction and beat feet to get there. They fearlessly break out the machete and find the way.
People may not want to follow a manager, but they join a leader without hesitation.
A friend of mine recently said that most managers esteem themselves as leaders. Unfortunately, that's all too true.