"Manager" and "leader" are distinct concepts, and they require distinct skillsets and personality characteristics. Probably the most concise distinction I can make is that a leader is the CEO (they set the vision for the organization), while a manager is the COO (they make the trains run on time). A leader is a change agent: their goal is to envision a better possible future and get people to buy into that future. A manager is a problem-solver: given a vision for the future, their job is to make that vision come true with a minimum of fuss and hiccups. Leaders need creativity, confidence, vision, persistence, and either really good technical skills (to build a demo and show people what's possible) or really good interpersonal & communication skills (to convince other people to build that demo). Managers need organizational skills, interpersonal skills, emotional intelligence, confidence, and really strong listening & communication skills.
It's fairly rare to find both skillsets combined into the same person. Steve Jobs was a great leader but a terrible manager; Tim Cook is a great manager but a terrible leader. Mark Zuckerburg is a leader; Sheryl Sandberg is a manager. Larry Page is a leader; Eric Schmidt is a manager. Steve Wozniak was a leader who had no pretenses for ever being a manager: one of the conditions for founding Apple was that he'd always stay at the bottom of the org chart. Jeff Dean is a leader; Sanjay Ghemawat is a manager (in a metaphorical sense, for both of them; they're both individual contributors).
Leadership often arises out of unexpected quarters: very often, it's strong-willed individuals at the bottom of the org chart who turn out to be the strongest leaders in times of crisis (and then they often rapidly rise through the org chart, at least as long as they find a good manager to partner with to make the trains run on time).
I appreciate the detailed response, I guess I've just been conditioned to equate "leader = manager" on account of their liberal and seemingly interchangeable use in job descriptions and roles (or perhaps that's my own misinterpretation). I do see the difference though, and think that I wouldn't mind being a leader as you describe it, and I believe I have most of the qualities you describe for it. I have thought of myself more as a silent leader (e.g. by example), or through peer coaching, but I am just wary of taking on a managerial role, and it sounds like for good reason: some of those qualities are my weaker points, and I plainly do not enjoy many of those things. Thanks again!
It's fairly rare to find both skillsets combined into the same person. Steve Jobs was a great leader but a terrible manager; Tim Cook is a great manager but a terrible leader. Mark Zuckerburg is a leader; Sheryl Sandberg is a manager. Larry Page is a leader; Eric Schmidt is a manager. Steve Wozniak was a leader who had no pretenses for ever being a manager: one of the conditions for founding Apple was that he'd always stay at the bottom of the org chart. Jeff Dean is a leader; Sanjay Ghemawat is a manager (in a metaphorical sense, for both of them; they're both individual contributors).
Leadership often arises out of unexpected quarters: very often, it's strong-willed individuals at the bottom of the org chart who turn out to be the strongest leaders in times of crisis (and then they often rapidly rise through the org chart, at least as long as they find a good manager to partner with to make the trains run on time).