That seems a bit disingenuous, since iteration and general recursion are fundamentally equivalent. So you could say that "recursion is just a special case of iteration".
Unless we're talking about specific iterations like iterating over a list, I guess.
Iterating over lists, or integers in a range is pretty straightforward. Iterating over a tree? What does that even mean? I suppose we could take "iterate" to mean a catamorphism. Under that interpretation, structural recursion and "iteration" seem pretty equivalent.
Just feels like quite an extension of what "iteration" usually refers to in a language like C.
ps: Also, a lot of programming is often conflated into 1-D. sed, grep, awk are mostly init ; iterate{ [PRED] FN }; exit
You're funny.
Equivalent in a computational sense.
Turing-completeness is a not very interesting standard.