A better discriminator might be global edits vs local edits, with local edits being things like retouching specific parts of the image to make desired changes, and one could argue that local edits are "more fake" than global edits, but it still depends on a thousand factors, most importantly intent.
"Fake" images are images with intent to deceive. By that definition, even an image that came straight out of the camera can be "fake" if it's showing something other than what it's purported to (e.g. a real photo of police violence but with a label saying it's in a different country is a fake photo).
What most people think when they say "fake", though, is a photo that has had filters applied, which makes zero sense. As the post shows, all photos have filters applied. We should get over that specific editing process, it's no more fake than anything else.