In modern knowledge work, leadership and management are more alike than different. The dichotomy between the two are more exaggerated than what reality suggests.
For all practical purposes, I have used the terms “manager” and “leader” interchangeably throughout my articles. When I mention leaders, I mean managers, leaders, executives, and basically anyone who is responsible for a group of human beings to deliver results.
However, in management literature it is common to highlight differences between the two. Two classic works are that of Kotter and Zaleznik.  
No one wants to be a manager
Our culture seems to give “managing” a lower status as opposed to “leadership”. No one aspires to become a mere manager but everyone wants to be a bold leader.
Lookup any brochure or website for an MBA program and the terms leader and leadership will be used far more often than the term manager. However, I have found the dichotomy false in my own practice.
I have yet to find a good manager who is not a good leader, or a good leader who is not otherwise a good manager. They both go hand in hand and the boundaries are not as distinct as we would like them to be.
Instead of distinguishing managers from leaders, we should be seeing managers as leaders, and leadership as management practiced well.
– Henry Mintzberg, Managing 
Leaders have to manage and managers have to lead. Although that would be the easy way out, I propose a couple of simplifying frameworks that might be helpful. One for both being the same and one for them being different.
The case for both being the same
Mintzberg suggests both being one and the same and for most people this is true.
Let’s stop the dysfunctional separation of leadership from management. We all know that managers who don’t lead are boring, dispiriting. Well, leaders who don’t manage are distant, disconnected.
– Henry Mintzberg, Enough leadership, Harvard Business Review 
There are as many definitions of leadership as there are writers. Some of them end up doing linguistic gymnastics in order to fit every eventuality and possibility into their particular version.
The case for both being different
Erhard et al, who differentiate leadership from management, suggest a very simple but powerful framework for defining leadership.
Being a leader and the exercise of leadership is all about realizing a future that wasn’t going to happen anyway.
When there is (or could be if looked for) a clear-cut pathway to fulfilling a concern, while it may require competent management to fulfill, it does not require leadership.
– Michael Jensen, Werner Erhard in Creating Leaders 
Plumbing as well as poetry
The reality, as any practicing manager knows is somewhere in the middle. It is not all about managing, neither is it all about leading. It is very situational and contextual.
The particular challenge or situation drives the need for either, and one responds accordingly without necessarily thinking about what particular modality one is in.
Leadership involves plumbing as well as poetry.
There are two essential dimensions of leadership: “plumbing,” i.e., the capacity to apply known techniques effectively, and “poetry,” which draws on a leader’s great actions and identity and pushes him or her to explore unexpected avenues, discover interesting meanings, and approach life with enthusiasm.
– James G March in On Leadership 
I will close this post with an excerpt from Ralph Stacey who looks at leadership and management through the lens of complexity sciences and chaos theory, and dismisses any simplistic cause and effect approaches to leadership and management. My position is consistent with his.
[T]his distinction between managers as traditional and rational while true leaders are charismatic is clearly an idealization and a rather simplistic one at that.
In reality, leaders do find that they have to attend to often mundane administrative tasks and managers do have to lead those who report to them if they are to get anything done.
For me, leadership and management are aspects of a legitimate power role in an organization and they cannot be separated. […] I will, therefore, usually use the term ‘leaders and managers’ as inseparable descriptors of an organizational role. Where I do use only one of the terms, I still mean both.
- Ralph Stacey in Tools and Techniques of Leadership & Management 
What has your own experience been when navigating the dichotomy? What have you observed?
- What leaders really do, and Management is (still) not Leadership by John Kotter in Harvard Business Review .
- Managers and Leaders: Are They Different? in Harvard Business Review by Abraham Zaleznik.
- Managing by Henry Mintzberg.
- Enough Leadership in Harvard Business Review by Henry Mintzberg.
- Jensen, Michael C., Werner Erhard, and Kari L. Granger. “Creating Leaders: An Ontological/Phenomenological Model.” Chap. 16 in The Handbook for Teaching Leadership: Knowing, Doing, and Being, edited by Scott Snook, Nitin Nohria, and Rakesh Khurana.
- On Leadership by James G March.
- Tools and Techniques of Leadership and Management by Ralph Stacey.