My leadership experience isn't horrendously far ranging or anything, but I see no harm in putting my $0.02 in here.
In my opinion, the difference between a manager and a leader lies in the fact that well, management is but one facet of leadership. A manager is rarely expected to be charismatic, etc. A leader is expected to show primary and secondary leadership behaviours. I once read somewhere, "Managers blame, Leaders take blame." (not infallible, but illustrates the point about integrity in a leader)
A manager, in the sense of the word, is someone who 'manages' a task, perhaps conducts planning and organization of resources, but is ultimately assigned these short-term tasks by a 'Leader', who seeks to achieve a long-term goal. The manager is expected to fit to a mould with his actions, while his Leader sets/shapes that mould.
Everyone's definition is different, googling/reading about Management vs. Leadership and drawing your own conclusions is probably the best thing to do, and to be honest, I don't see anything wrong with your definition anyway.