A task manager is a software utility to manage day to day activity. It helps achieve specific goal or goals of individuals or groups. These software are useful for individuals working on project or groups of individuals collaborating and sharing knowledge and work for the accomplishment of collective goal(s).
What is GTD?
From Wikipedia:
Getting Things Done (GTD) is an organizational method created by David Allen, described in a book of the same name.
The Getting Things Done method rests on the principle that a person needs to move tasks out of the mind by recording them externally. That way, the mind is freed from the job of remembering everything that needs to be done, and can concentrate on actually performing those tasks.