As you brought up. Genius doesn't mean greatness, and vice versa. They are orthogonal, although genius can help make someone truly great.
To your other point, I've worked with a lot of "gifted" kids, and one thing they all seem to share is the ability to completely block out the outside world, even forgetting to sleep and eat, when they are working on something interesting to them. This is not *generally* a trait I see in other kids (or adults, for that matter).