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.
Edit: reference: https://beza1e1.tuxen.de/waterfall.html
TLDR: the original impetus for waterfall is basically what we call agile today.
Someone copy-pasted a random chart from a paper (one the paper specifically said was too problematic) into a DOD process spec, that turned into a standard because the DOD loves to standardize everything, and big companies all adopted the fundamentally flawed approach and called it waterfall.