The biggest difference between Agile and Waterfall is the approach that each offers towards project management and development.
Waterfall is a linear, step-by-step process in which each of its stages, including planning, design, development, and testing, must be fully completed before proceeding to the next. It requires detailed upfront planning and is rigid in structure, making it harder to accommodate changes once the project is underway.
Agile is an iterative and flexible approach that focuses on delivering smaller pieces of the project (increments) in cycles of work (sprints). It promotes regular feedback, allowing for continuous improvement and adaptation, which is a much easier way to adjust to changes within the project.
To keep it short, Waterfall is a sequential, step-by-step process, whereas Agile involves agility, interaction, and incrementally.