If we hypothesize that neither Scrum nor Agile are project management, then what are they and what is their relationship to project management? Answering these questions requires defining several terms.
I have previously defined Agile as sets of values and principles governing software product development methods given in a document called the Agile Manifesto. The manifesto provides a list of value statements or preferences about how to conduct software product development but does not provide any specifics on how they should be implemented. Similarly, Scrum is a specific product development method based on Agile principles. Scrum focuses on the design and build portions of software development, provides a specific vocabulary and process elements, and is based on a collection of assumptions which includes Agile values as well as others related to the team, the product, governance, etc.
While I like the definition of project management given by James T. Brown as “the application and execution of structured, organized, common sense,” it is more rigorously defined in the Wikipedia as “the practice of initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria at the specified time.” That is, project management is a set of processes used to meet identified goals that apply to a broad range of fields of endeavor. The PMI PMBOK is a broadly accepted description of project management.
So, Agile, as a set of principles rather than processes, cannot be project management. Agile philosophy can be applied to project management as seen in second generation methodologies like SAFe and Smith/Sidky, but do not provide a complete framework from which to derive project management approaches as is found in the PMI PMBOK.
Finally, Scrum can be viewed as an intersection of Agile principles and processes for software development and so might be confused with software project management. It focuses on the planning, executing, and controlling elements of software projects, defining how those elements are managed. However, there are significant elements of software project management that Scrum does not address. For example, key elements of the initiation phase like establishing the project goals and deliverables, gathering the resources, defining the development methodology, and gaining sponsorship and approval are either not addressed or assumed to be present prior to the start of the project (without saying how). In addition, elements like architecture, environment construction, risk and issue management, change management, and the close phase are critical activities in managing software projects that are not incorporated into the Scrum method.
So, if someone tells you about their Agile or Scrum software project, they are giving you only a partial description of the activity. Either they are giving you the philosophical context of the project with no indication of the specific processes, they are omitting some of the processes being used to manage the project, or they are acknowledging that they aren’t managing key elements of the project at all.