> Actual waterfall looks very much like actual agile, in that it is designed around iteration loops. The primary difference is that waterfall prescribed steps in the iteration process, and agile is just a set of principles in a manifesto.

In that case, I don't believe companies follow either. I've never seen anything as principled (in any form) practiced anywhere.

Companies claiming to do Agile were usually doing some rituals and cosplaying as agile. I don't believe I've ever seen a company doing "waterfall" or anything resembling what your link describes either.

They mostly do chaos-driven development.