The Scrum Master role

Scrum Masters are those who fully understand Scrum, and help the Scrum Team by coaching them, and ensuring that all Scrum processes are implemented correctly.

The Scrum Master is a management position, which manages the Scrum process, rather than the Scrum Team. Is a servant-leader for the Scrum Team.

Besides ensuring that the Development Team understands and uses Scrum correctly, the Scrum Master also tries to remove impediments to the Development Team, facilitates their events, and trains and coaches them.

The Scrum Masters help the Product Owners too, by helping or consulting them on finding techniques, communicating information, and facilitating related events.

The responsibilities of the Scrum Masters are not limited to the Scrum Team. They should also help those outside the Scrum Team understand the appropriate interactions with the Scrum Team to maximize the value created by the Scrum Team. The Scrum Master usually leads the organization in its effort to adopt Scrum.

There is not Project Manager role in Scrum, and none of the 3 roles of Scrum (Product Owner, Scrum Master, Development Team) act as a traditional project manager.  

Sometime  people consider the Scrum Masters to be the equivalent to traditional project manager,  but it is not true, because the Scrum Master responsibilities are very different than a traditional project manager.

The project management responsibilities are distributed among the three roles of Scrum and there is no centralized project management in Scrum.