If you look closely, all three of your lists have steps involving pointing and shooting. I rest my case.
As for the difference between auto-focus and “point-and-shoot” cameras, I could care less. I only suggested calling them auto-focus, too, because everyone suddenly started talking about the all-important step of focus. Call it auto- anything. Because that’s its most important attribute, correct, that it does everything it can on its own.
If you look closely you’ll see that there are no other steps on point and shoot, that in fact the name is also the complete list of directions. Thus showing you have no case.
If this is actually something important to you, and not just you being a curmudgeon, the difference between point-and-shoot and auto-focus is important to you. Because they actually are two different types of cameras. The cameras aren’t “auto-anything”, that would actually be exactly the kind of name you’re saying (incorrectly) that point-and-shoot is, without meaning and expressing nothing. The most import attribute of a point-and-shoot camera is that the label is the directions, you do nothing to it before pointing, and you do nothing between the pointing and the shooting. They are point and shoot.