The Agile and Waterfall methodologies represent two distinct approaches to project management. Waterfall is a linear and sequential model where each phase must be completed before the next begins. This model is best suited for projects with well-defined requirements that are unlikely to change. In contrast, Agile is iterative and incremental, allowing teams to adjust and refine their work as the project progresses. Agile's flexibility makes it ideal for projects where requirements evolve over time. The main differences lie in their adaptability, risk management, and stakeholder involvement. Agile fosters continuous collaboration and adaptability, while Waterfall emphasizes thorough documentation and predictability.