ADDIE is covered in depth on this site. ADDIE is the 5 elements of creating learning in the Systems Approach to Training. It is as effective today as it was 25 years ago. Agile is traditionally a method of managing the development of software. Agile could be used as a subset of ADDIE in cases where the training product (software) is subject to several iterations and can be released incrementally. Agile came into vogue at the same time software went to a constant release (subscription) model in the early 2000s.
Agile dictates that software is built incrementally from the start of the project rather than attempting to deliver it all at the very end. Each project is broken down into smaller, bite-sized functions and are prioritized and given to different user types. Then those smaller mini-projects are continuously worked on and delivered over short spans (like two-weeks) and called iterations.
Very few Learning and Development departments in organizations are set up on an Agile Project Management life cycle. Nevertheless, the concepts of Agile project management may apply in certain training products that are frequently updated or released. Just in time training on the latest use of software may be, for example, set on an Agile pathway just like the software the training covers.