Waterfall is a caricature straw man process where you can never ever go back to the drawing board and change the requirements or specifications. The defining characteristic is the part where design up front, you can never go back and really really have to do everything in strict order for the whole of the project.

Just having requirements and a specification isn't necessarily waterfall. Almost all agile processes at least have requirements, the more formal ones also do have specifications. You just do it more than once in a project, like once per sprint, story or whatever.