DevOps
Dev for developer is a team who build the the application or code that application.
Developer responsibilties are Planning about application coding for this application, building this application, testing/checking this applictaion for checking bugs, releasing/handover this application to the operation team for deploying.
Ops for operation: is a team who is responsible for deploying that application which is build by developer
operation team responsibilities about the application which were deployed on server and accessible for users, operating the application mean management, monitoring, and maintenance of application to ensure smooth and realiable for users, and the last step is monitor that is the process of checking the
application if there is any problem bugs or any other thing that is problem for end users.
Agile
Agile is a iterative and flexible. In this method the projects broken into pieces which are developed and tested in short cycles. In agile the benefit is that we make changes during the development process. The choice between them depends on the project needs such as clarity of requirements and necessity for flexibilty and periodically. When the requirement are not clear or there is doubt that the requirements change or something else then agile method is best. Agile is gernerally better in modern software because it allows to change requirements anytime.