I'm not up on all the canon, but as I recall, the original superman was simply from a high-G world, superhumanly strong, fast, able to leap tall buildings (tad derivative of Burrough's "John Carter," if you think about it) - but not fly or fry eggs by staring at them, and not quite supernatural. At some point he got retconned to the explanation that his powers were psychokinetic and powered by the energy of the yellow sun - and, he crossed that line.
Though it's not entirely cogent there's also a line between impossible, for an unaided human (dead-lifting tons), and logically impossible (meaningless), God creating a stone He could not lift.
And your vehicle for that is the 'twighlight' case of the impossible - because something impossible may be superhuman (day), like leaping over a castle wall, and something supernatural (night), like dematerializing and walking through a castle wall would certainly be impossible, then the two must be the same (night = day, because: twilight).
Yes, because it's a quite easy category difference.... Meaning is arbitrary, if you get right down to it, all language is symbolic, but no, it's a very clear test and easy to apply consistently. That is NOT what teleportation is, though. Teleportation is moving from one point to another without passing through any other points on the way. Teleportation is supernatural. A teleport mechanic, in an effects-based game like Hero, might be used to model a non-supernatural power, but it would generally have a limitation placed on it so it did actually include more natural movement - for instance, a super-escape-artist might buy a teleport to escape from impossibly difficult confinement, but the 'effect' would still be wiggling out of it, not moving without traversing space. FWIW.
Not actually that far off base. In Mage: the Ascension, for instance, magick can be covered with a coincidence, so if you wish for a million dollars and win the lottery, you're fine, but if you just conjure the money out of thin air in front of everyone, you can invoke some paradox. Not the exact same distinction, but very similar - it's more about how the effect looks. Supernatural is more about how the effect happens, it's really little to do with degree. In the case of Wish, earth-shaking magic is, indeed being invoked - supernatural as all heck.
For instance, aporting a silver piece from your purse into you hand is supernatural, even though it's a trivially easy and natural thing to just reach into your purse and pull out a silver piece - and, even though sleight of hand could appear to do the same thing.
When you get right down to it, entering orbit is just an incredibly powerful leap.
Sure, and a certain point, the supernatural - starting a fire pyrokinetically for instance - becomes just as trivial as striking a match. Possible vs impossible, degree of power or believably really has no bearing.
I think it's more reasonable, in the case of oh-so-inclusive 5e, to say that neither of us has any right to say the other's preferences should be excluded from the game. And, what do you have against the famed Florentine fencing style?
Oh, I'm fine with that. I was just pointing out that your opinion that one 4e fighter power should have been supernatural in no way alters the fact that no fighter power in 4e was supernatural. The editions have offered different menus of non-magic-using classes. AD&D PH had the Fighter & Thief, both 100% non-magic-suing. 3e PH had the Fighter, Rogue and Barbarian (EX powers but no SU, quite explicitly), likewise. The 4e PH had the Fighter, Ranger, Rogue, & Warlord, likewise, 100% non-magical. 5e happened to give every class at least some magical powers, though, it does have specific Fighter, Rogue and Barbarian sub-classes that do not. AD&D, 3e, & 5e all limited their non-magic using classes to DPR and skill-specialist roles - 4e was unique in letting them cover 3 of it's 4 formal roles: Defender (aggro), Striker (DPR - and, incidentally in the case of Ranger & Rogue, skill-specialists), and Leader (support). While Martial lacked the Controller role in 4e, it was a fairly seamless thing to run a campaign with only martial PCs, whether the world was high-, low-. or no- magic - 5e isn't as far away from that as other pre-4e eds, but it could be closer, and 6e certainly could go there if it wanted to...
...Templates could help. Having a 4th (after Race, class & background) major choice point for PCs could give more flexibility in creating a fully-functional party in spite of concept or campaign limitations on what sorts of characters might be appropriate...