I would argue Agile is a Philosophy and Waterfall would be more of a Methodology. My biggest concern with Agile is that it's lacking integration with a methodology (ie: best practices of waterfall could be in an agile way). Companies and teams tend to just say lets do Agile/Scrum/Kanban and leave out the requirements definition, documentation, etc and replace it with "As a user create shiny button". Which, might be fine in some cases but as a new-start it lacks direction IMO.