A leader is someone who can influence followers to work fully towards a mutual goal or gain while a manager is someone who is tasked with making things happen on time in a certain way. A manager doesn't always have authority but they are given power over the people they are managing so they can get a task done. Scrum masters and product owners would have to be both manager and leader since although a leader can get people to follow them, they need at least some managerial skills to handle things like deadlines and problem causers.
I am sure that leadership is a skill that can be learned and I have always been pretty sure of it. There is probably a set of genes which, if someone grows up in the right environment, will allow people to be great leaders, but Leadership definitely isn't just genetic as evidenced by the thousands of inheritors who squandered their parents authority, power, or money. I've also seen people become better leaders simply through practice in groups at school.
Hunter keeps talking about influence because it is central to being a leader. People in charge can have different kinds of influence over others; there's the "I'll get fired if I do this wrong" influence, the "that guy helped me out last week so i'd love to reciprocate" influence, and many others. The kind of influence you have with your workforce shows what kind of a leader you are.
I have earned a not so small amount of authority in school based concepts. This is especially true for math since I have consistently done well in the subject and helped other people to do the same. I also have a significant amount of authority with my brother since I have on more than one occasion covered for or helped him in situations which he didn't necessarily know how to deal with.
Using power to make others accomplish a task is actually somewhat difficult on FRC teams since there is little to threaten a dissenter with. Obviously somebody could be kicked off of the team or removed from a project, but since the entire FRC experience is on a voluntary basis and we really need the people we have, both of those are unlikely. Thus, we should only use power sparingly. If someone is preventing a deadline from being reached or causing arguments, power could be used, but just as equally someone could simply tell them what is going on and try to work it out.
In these chapters I learned a little bit about the difference between managers and leaders, the difference between power and authority, and how your influence with your employees depicts your leadership or management style.