When I was in the Navy we used to have a saying, "We have chiefs, and we have E-7's. The chiefs are leaders, and the E-7's just get to wear the khakis and the anchors on their collars."
The gist of that point is that manager is a title, and leader is a personality trait. You can have the title, but it doesn't automatically qualify you to have the personality trait of a leader.
I would go on to say that, unfortunately, most managers I have met are not leaders.