The word Agile usually refers to the philosophy behind software development. There are multiple flavors of Agile. Agile values and principles are put together to form the Agile Software Development Manifesto and the different Agile principles.
Agile development is an umbrella term describing several Agile methodologies. Some of the well-known methodologies are Scrum, XP (Extreme Programming), Crystal , FDD (Feature Driven Development), DSDM (Dynamic Systems Development Method), and Kanban .
Each of these methodologies has a slightly different approach to implementing the core values and principles behind Agile Manifesto and principles. They all fundamentally incorporate communication, collaboration, continuous feedback, continuous testing, continuous interaction, continuous prioritization, and planning with continuous improvements to deliver solutions for a customer with changing requirements and businesses.