Compared to these other styles of leadership, the director style is much more forceful and authoritarian. It is very much a top-down style of leadership.
By contrast, the other types of leaders allow for much more input from their subordinates. In the problem-solving style, the leader is much more of a facilitator. The leader will take suggestions from subordinates and will entertain various ideas about what will work. The delegative style goes even further. In the delegative style, the leader simply gets out of the way. This leader lets the subordinates do the work and does not try to tell them how to do it.
All of these have their strengths and weaknesses. The more authoritarian the style, the more likely it is that things will get done on time and in the way that the leader wants. However, subordinates may feel very unhappy and demoralized. The more we move towards the delegative side of the spectrum, the more the subordinates feel values. However, this type of leadership can be unfocused and lead to delays and confusion in trying to get things done.