In my experience, leadership and management are pretty disjoint. You can be good at one and not good at the other. Although, FWIW, I suspect that your introspection about whether or not you're a good manager means you're a lot better than you're giving yourself credit for.

Agree, they are different. Middle managers particularly don't have to be leaders, and in many cases shouldn't be. But for things to work well, they do need to be good at management with all of the people skills, cat herding, and organizing that go along with it. In my experiences, the best managers were the ones who protected their teams from the whims of the 'leaders' at the higher levels. The worst ones were the ones who carried out their every wish without a second thought.