When talking about management, what most people are thinking about is efficiency, maximizing output per unit of input. Many (most?) people talk about the need for leadership in addition to, or even instead of, management.
But what exactly do we get from leadership? What is its purpose?
The first word that comes to mind is “effectiveness”. But most measures of effectiveness are based on a desired end-state, which to me makes this just a different way of measuring efficiency.
Is leadership just another way to get people to do what you want them to do so you can accomplish your own goals? Or is it something different, something more?
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When you “manage” something / someone, the best you can hope for is what you ask for. When you “lead” someone, there is no way to know ahead of time what you will end up with.
Maybe the question is better addressed in the context of the Cynefin framework:
Management : Simple :: Leadership : Chaotic
(and possibly disorder), with a sliding mix of the two being appropriate in complicated or complex situations.
Of course, I’m not the first person to consider this question. There are many (many many) more thoughts on this question out there, as you can see in the Google search results for leadership vs. management.