Agile is a general philosophy describing a set of guiding principles for building software through iterative development. Agile development is about providing a framework that allows developers to build something useful for real world users and deal with the realities of interruptions, timelines, and technical requirements that disrupt an ideal development cycle. In other words, Agile development helps developers deal with reality.
SCRUM is a methodology -- in another words, an implementation -- pertaining specifically to project management. Other "Agile" methodologies inclue extreme programming, kanban.
Scrum was a term first used in 1987 to describe hyper-productive product development in Japan. The word Scrum comes from rugby, where scrum refers to the strategy used for getting an out-of-play ball back into play. The name Scrum stuck because of the similarities between the game of rugby and the type of product development prosc