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.

… or at least it always used to be hard to ‘lead’ a server.

But now that the server has an agentic interface maybe that is changing.