An Agile development methodology is essentially just another potential way of applying or approaching Agile project management / development in general. But before we get into specific examples of methodologies, let’s back up and examine what Agile development is.
Agile development is a system for managing projects, particularly software development that evolved out of the older system, often referred to as “waterfall software development”. The hallmark of Agile is its “lightweight” approach to managing individual / specific elements of any project. You see, in previous incarnations of software development, intense, stifling micro-management was fairly commonplace. Over time, it became obvious that this older system was not as efficient or personnel-friendly as it could be. Agile is merely a similar but superior system for software development, for all involved parties (including managers, developers, and customers).
Over time, individual methodologies were created to help deal with specific types of problems and projects. For example, some projects might have more stringent requirements or deadlines than others; those projects might be better suited toward RAD development. RAD development, or Rapid Application Development, is a means of producing a more completely functional prototype in a shorter amount of time.
Of the many types of Agile development methodologies, Scrum is arguably the most well known (and perhaps, used). What sets Scrum apart is its system of mini-deadlines / meetings which not only encourage collaboration, but also creates the need for incremental developmental successes. Scrum basically takes individuals, forms smaller groups of developers from them, and then assigns them incremental tasks to complete. At the end of each “task”, all the individual teams are united where results are shared, problems addressed, and the next line of goals, laid out.
Simply put, an Agile methodology is a specific manner of applying Agile techniques and systems of organization.