"Keto" is pretty straightforward: it is a delicate, metabolic state in which the body produces a hormonal response to induce lipolysis to produce ketone bodies for energy in the absence of dietary carbohydrate.I think "Keto" is the wild, wild west. Kinda like Indiana weather, just wait, and it will change.
Can that be done with both processed and whole foods? Yes. Both modern and primal/paleo foods? Yes. Do those things matter? Probably - but they don't change the mechanics involved in inducing metabolic ketosis.
Personally, I stick as much as possible to whole foods. The only thing close to processed food that I eat with any frequency are pork skins. I've mostly dropped even mayo and salad dressing from regular consumption, because I have otherwise cut out all vegetable/seed oils (highly inflammatory), but really don't like the taste of commercial, avocado oil-based dressings. (Might experiment with making my own.)
But, I do those things as part of a strategy to reduce inflammation - a strategy that coincides with, but is separate from, keto.