In reply to Toby S:
To me, leadership is going somewhere, and getting people to follow you. A leader goes first.
This may be a physical thing, but is more likely to apply in terms of ethics, attitude, diligence, keenness to learn. Of course, people can lead in any direction, so you can lead people to become lazy, dishonest, violent, etc. I think of Tony Blair's leadership in the use of violence to solve problems (Sierra Leone, Afghanistan, Iraq), being happily carried on by David Cameron (Libya).
Management is from the Latin, manus, meaning hand, and originally referred to controlling a horse or team of horses through the reins. So management is controlling the actions of others by wielding the reins of power.
Both can be learned.
As importantly, both can be forgotten, and often are once a person gets into a position of power and gets sloppy.
It is worth remembering that "the manager" need not be the only person in a team with leadership skills, nor with management skills. Some people become very skilled at managing their boss and leading the organisation in a way they think it should go. The best ones do it in such a way the boss never notices.