Saying “Managers care about efficiency and leaders care about effectiveness” is like saying “Doctors care about theory and nurses care about patients.”
Managers that don’t care about effectiveness are lousy managers.
Leaders that don’t care about the gemba are lousy leaders.
Doctors that don’t care about patients are lousy doctors.
Nurses that don’t care about theory are lousy nurses.
Your role in the organization (and for the particular situation in question) and training and the situation will impact how you contribute. But the attitude that leaders are visionaries that think big thoughts, make decisions then tell everyone what to do (act as the brain for the organization) is outdated. Every list of what traits are for leaders that then contrasts them with managers that I have seen shows leadership traits managers need.
Seeking to separate leadership and management is a bad idea. If you want to have a few leadership traits that you want to focus on at various points (creating engagement, communicating a vision, building consensus, setting organizational direction) that is fine. But those things are traits managers need; they are not traits reserved for some separate leadership cadre.
And disconnected leaders that don’t understand the organization, the organizations customers etc. are not going to lead well (normally the contrast lists have the managers doing all the hands on stuff, at the gemba, with customers etc.). Nurses may not have as complete an understanding of the theories behind medical treatment decisions but they need to know a great deal of theory to do their jobs well. Everyone contributes and has different roles to play but I don’t see value in the contrast of leaders and managers mentality.
From what I have seen mainly the manager v. leader comparisons seem to be about belittling managers and elevating leaders; but leaders are this vague concept that isn’t well defined. Who are these leaders? Are they only senior executives? They can’t be managers because you are contrasting them with managers – by the contrasting model used they can’t be leaders and managers.