Agile and DevOps tend to coincide on certain aspects. As and when the age old waterfall method began to lose its charm with constantly changing demands the need was felt for a more flexible approach.
The Agile methodology works on the core principles of elasticity, instancy, people and their interactions. The idea of Agile focuses largely on the developers having to break down the entire process of development into multiple user stories and constant delivery to the customer rather than emphasising on a finished product. The process involves several smaller feedback loops.
DevOps lays focus on communication internally as well as between departments so as to ensure transparency, increase effectiveness and smooth functioning across teams.