I'm going to disregard the turning element of any kick, just focussing on a kick to the rear.
Does your style differentiate in terminology between rearward kicks if the chamber and finishing angle of the kicking foot is different?
Example, to me a back kick is: the hips stay mainly square throughout, the chamber is directly in line and the kicking foot finishes at between vertical and 45° (toes below heel).
A "back side kick" (or whatever): the hips turn slightly, the chamber is biased to the side a bit and the kicking foot finishes horizontal (toes level with heel). You don't finish fully side facing, but more so than with a back kick.
Our terminology isn't based on position of the foot, rather on the kick itself. American Karate is an eclectic system. In the pic below, on our wedding day, my wife wanted a kicking pic, so we took one. She's throwing more of a sidekick similar to a Korean stylist, I'm throwing an American sidekick. We teach sidekicks in a lot of different ways, you learn them all, and find out which ones do what. She can hit with hers quite well, as can I. In competition, sidekicks were both our money kicks, yet they were totally different.
She likes to point out that she's throwing the better kick. I like to point out she's looking at the Peanut Gallery instead of her target.
In all of our kicking, the primary focus is on end result. All of my students kick a little differently, especially Black Belts.
Take two people, one starts his Martial journey with no flexibility whatsoever, the other, really flexible. It would be nice to think the tighter person will catch up flexibility wise, and he'll certainly loosen up some over the years, but in reality, he's more than likely never going to be as loose. His kicks are always going to be different than the other guy's. But he's still going to learn to hit with them. Just have to train him differently.
If you can kick me in the chest and knock me down, or whatever your goal is with the kick - create distance, injure, part of a combo, whatever - I don't care what position your foot is in, as long as it's not detrimental to your body or to your game. I just want you to be able to apply it to someone who doesn't want you to.
