First Scrum is definitely not a project management methodology, it is just a framework. As for agile, it is still debatable on whether should it be considered a methodology or not.
Now Scrum is a project management framework that falls under the Agile methodology, and Scrum is only used (so far) in software development projects. Scrum defines the roles, the responsibilities, and standardizes communication in the project, and rigorously follows Agile's incremental and iterative approach to managing projects.
So, Scrum, in addition to other frameworks such as XP and RUP, all fall under the Agile umbrella and inherit Agile's common traits.