Adding more thoughts to the below answer, let's examine the project manager's role and responsibilities.
The project manager's role is to manage the project.
The project manager's responsibilities is to do the following activities in order to manage the project (see how the role is related to the responsibilities):
- Create the project documents
- Manage the project schedule
- Manage the project team
- Manage the conflicts/risks/issues
- Manage the project sponsor/the client/the stakeholders
- Report about the project
- Close the project
Of course there are many responsibilities, but as you can see, all the responsibilities fall under the same role.
It is possible to have two roles per person, for example, a Program Manager (whose role is to manage a program) can also be the Project Portfolio Manager (whose role is to select and prioritize projects).