Many of the best CEOs are both a leader, visionary and a strategist.
What’s the difference? Leaders are willing to go ahead of people and can inspire. Vision helps them to imagine possibilities. Their strategic nature allows them to see how it all fits together.
This is great for CEOs, because a CEO catches the existing vision of the company, interprets that vision through her own eyes, and then sees the general direction and general strategy potential (taking into account research and seeing the big picture). Then, using her understanding of morale, she inspires her team to do their jobs in pursuit of the goals.
But “leaders of men” are not always great strategists. Some of them are simply great public speakers that drive their companies or countries into the ground. And a great strategist never gets off the ground without being able to get people on the same sheet of music. And millions of homeless people are visionaries (who never push hard to get their vision tested, which is part of the learning/growth process).
So you could be a visionary and be homeless. But strategy purifies vision (through theoretical bench-testing (thought experiments) and building a big picture). And leadership activates people around that strategy.