Agifall is an approach that uses more-thorough research and planning stages to build tasks, and then relies on sprints to see those tasks successfully carried out. Agifall is essentially the Agile methodology, but with more focus on upfront research.
Wagile is a term used to describe an approach where a project incorporates certain aspects of the Agile methodology into the Waterfall process. Unfortunately, the term has developed a somewhat negative connotation, implying that an organization is trying to apply Agile principles, such as daily standups and short iterations, without making any significant changes to how the project itself is carried out. Still, some businesses find success with the Wagile approach, organizing each sprint into smaller waterfalls of subtasks that must be completed in a specific order.