Managerial effectiveness, in short, is the ability of a leader to get results out of his or her staff. A good manager has a unique set of skills and abilities that he puts to use as a leader and organizer; the effectiveness of his job depends on how productive an organization can be under his or her stead. Whenever a leader achieves results, they are displaying managerial effectiveness; the effective leader is aligned with the culture of the organization and its goals, and makes sure that they have the right skills to get the job done. People, conceptual and technical skills all come to bear to provide effective managerial leadership; a manager has to be able to work with people and develop new ideas to maintain a good workflow and achieve objectives.
Managerial efficiency involves the overall productivity of the firm under a manager's command - how well they can use the resources available to them with the greatest use of the company's time. This concept can be identified as coming from three places - having a great an initial endowment as possible by management in order to get the ball rolling, gathering as much knowledge as possible, acquiring skills in the process, and having as many good resources as possible within the firm. A manager with good managerial effectiveness will most likely produce a firm with the highest managerial efficiency; while effectiveness is determined by the manager him or herself, efficiency is the overall output that a manager provides his or her firm.
References
Certo, S.C., & Certo, T. (2008). Modern management: concepts and skills, 11th edition. Prentice
Hall.