How a project is managed depends a lot on how much control a project manager has on the project and that relates with the type of Organisation in which the project manager is working.
There are different types of Organisations, namely:
1) Functional Organisation: In this kind of Organisation, the project team members report to a functional manager who calls all the shots. The project management related decisions need to be cleared by the Functional manager. Project managers mostly work as assistant to the functional manager. They spend most of their time in administrative tasks. You are likely to find project expediters (who keep track of status and have no decision making capabilities) in such type of an organisation.
2) Matrix Organisation:
a. Weak Matrix: Here Project Managers have some authority but the resources still report to the Functional managers. Major decisions are still taken by the functional managers. Such a type of organisation can have project expeditor or co-ordinators (who can take some minor decisions).
b. Balanced Matrix: Here, Project Managers and Functional Managers share equal authority. While Project Managers run their people management decisions by the functional managers, the functional managers run their Project Management decisions by the Project Managers. Here, the project team members report equally to the project manager and the functional manager. In this case, the project manager has comparatively more authority as compared to the previous models discussed.
c. Strong Matrix: Here, Project Managers have more authority compared to the functional managers. The project team members still report to both the functional and project managers. Though the team performance is measured on both their project and functional skills, more weightage is given to project delivery.
3) Projectised Organisation: Here, the teams are organised totally around projects. The project manager makes all the decisions about the Scope, cost, time, quality, resources and risks. Once the project is completed, the resources are freed and then used for the next project. And finally, the project manager is responsible for the success or failure of the project.