I think of leadership as distinct from management. Importantly, I think you can be in a position of leadership without needing to be in a position of management.
Management requires direct reports: you make decisions which directly impact the careers of other people.
Leadership can be more subtle than that. You can influence people without needing to directly manage them.
John Carmack at Facebook/Meta is a great example. He was an IC - they had to invent a new level of the IC ladder for him! Definitely a leader, not a manager (at that company).
(Amusingly, I got to attend some "leadership" classes at Stanford a while ago. My main takeaway was that the way to create leaders is to put a bunch of people in a room and tell them that they're "leaders" until they start to believe it.)
Being picky with words, you can be a manager of something other than people, it is the same broad skillset. Managing people has a few skills that are people-specific, obviously. But you can manage servers, manage widgets, etc.
Which makes it clearly distinct from leadership, because it is very hard to lead something that isn't alive. It is hard to lead a server.