On Authority vs. Leadership, authority is something that is granted and/or acknowledged. For example, a manager in a company may have authority. That authority has scope over a particular set of decisions. Leadership is different. It is the use of power and influence to move others towards a goal. The levers they use could include force, persuasion, passion, charisma, reward, punishment, etc. One can be a leader without authority, and one can have authority but not be a leader. Leaders use a variety of different levers, as mentioned above, and the ones they use will vary based on the situation. Sometimes it's about expertise, sometimes it's about charisma (power + empathy). The most stable leaders will be operating through reciprocity. In the first post you mention someone who leads by strength. Their position is tenuous and they may be hated by those who follow them. They could lose their position at any moment. But a leader who is respected is more likely to stay in power, and often that's how things settle out, because the bad leaders get replaced until someone who can do the job gets it. (As an aside, respected by who? By the people who are closest to them in the hierarchy. The average peasant may hate the king, but they may support their villages chieftain, who supports the local count, who supports the duke, who supports the king. More on how this works can be found here:
Basically second what @Matt E said. Another thing I'd add is that there are different leadership styles, and everyone naturally inclines to one or maybe two of them but no one is naturally adept at all of them. However, there are always situations where one style will work better than another, so becoming a good leader is about learning how to flex into a style that isn't your natural tendency. At the last leadership training I took they had a handy typology of styles but of course they escape me now. But some of them were ie visionary (focused on achieving a goal), affiliative (focused on the well being of your people), coaching (focused on doing things in a certain, right way) etc.
One thing that's often overlooked is that it isn't all power and privilege—authority comes with responsibilities. Also, the very word includes Author. An authority is expected to know what they're doing, to have deep and broad experience in their field arising from a great deal of knowledge.
And sometimes a person without much personal authority is promoted to a position where they're in charge. Like this fast food assistant manager:
