The agile methodology uses iterative approaches to get faster results during the development process, while Scrum is a type of agile framework that helps organize teams.
Project managers and scrum masters are very different people. The project manager is in charge of the project, while the scrum master implements the Scrum principles.
Agile is a type of development methodology, while Scrum is the type of an agile framework.
They share some functionalities, but there are some functions they do that differ from each other.
It depends on your interest. If you want to manage the whole team and other stuff like finances, you go for the project manager, while if you want to implement the Scrum principles, you become a project manager.