Exactly! It's almost as though the defining characteristic of supernatural phenomena is that they're not real, or that people just say, "Hey, it's magic," and leave it at that.
Actually, it seems to me that not being real and belief in magic are two fundamentally different things. E.g.,
aether or
phlogiston turned out to not be real, but there was nothing even vaguely resembling belief in magic in either theory. In fact that's why they could be falsified: there was no expectation of anything else than reproducible natural phenomena there.
It seems to me that for something to be belief in the SUPERnatural, there actually has to be a SUPERnatural component. I.e., something that supposedly can't be explain by just normal matter and physics.
Basically think of the following example: Think if I were a 19'th century explorer and sailed a brand new steel battleship (like
La Redoutable) to some new island in the pacific inhabited by a tribe who never met any other humans and never saw a boat bigger than a canoe. Let's say they can think as rationally as they can about it. They know how to make a canoe and they're sure that long before that size, it would break in heavy waves. They can also know that there is no tree whose trunk I could hollow to make a battleship-sized canoe. The ship though clearly exists. What matters is how they explain it.
A. If they think it can be explained by materials and construction techniques, that's not a supernatural belief. Even if it involves non-existent hypothetical entity, like they imagine there are giant steel trees from which such ships are made, as long as they think there is some natural explanation behind it, it lacks the "super" part of "supernatural."
B. If they think that there is an element of appeasing great spirits, or using secret words of power, or whatever, that's belief in supernatural.
The two may be indistinguishable when it comes to explaining how that mighty ship came to be, but nevertheless there is a fundamental difference there.
The former doesn't depend on human wishes or relationships with the spirits or anything. That ship could be made by mindless robots, and predictably it would still sail. It's just the natural properties of the materials and components, tell you that it can sail, and what kind of forces it can shrug off.
The latter is fundamentally something where just the material properties of something aren't enough to make a prediction. A worse ship could sail just fine if the great spirits wish so, and a better ship could break if the spirits are hostle. There is some element, be it a god, or a spirit, or a ritual, or a word of power, or just the power of wishful thinking, or an entitlement delusion (e.g., the universe owes me a good trip because I have good karma), that can take the laws of physics to take a break. And it's invariably a fundamentally untestable and unfalsifiable element. Measuring twice before building the ship wouldn't help, if the great spirit of the sea still doesn't want it to sail.
And to further illustrate the difference between just belief in something that doesn't exist, and belief in magic, consider this: consider that i now were to tell those tribesmen that, nah, mate, this ship ain't the biggest in the world any more. The English built one twice as heavy by now. The English in fact had no such ship at the time, so if those guys believe me, they believe in an English ship that doesn't actually exist yet. But that alone doesn't make it belief in the supernatural. If they believe, basically,
A. "Damn, those English guys must be real skilled at building boats."... then that's naturalistic thinking.
B. "Damn, those English must have some mighty shamans, who know how to appease the spirits of the wood and of the sea, to make such a big ship sail."... that's supernatural thinking.
Someone at this point may note that the distinction is a bit pointless, since all technologically primitive cultures would not have a naturalistic explanation of the universe, so they'll only come up with the latter kind of explanation. (And indeed, even at late antiquity levels, the Greeks were the only culture we know of where some people had ideas that some events can be explained 100% by natural causes, without involving any spirits or gods whatsoever.) But far from being pointless, that's the point: then they only have a supernatural view of the world, and lack a scientific view.
Or in the same vein, consider the following example:
1. If I'm a smith and see for the first time a beautiful katana, and learn of the ritualized way to make tamahagane steel and hammer it into a sword. If my thoughts are:
A) "Damn, I must find out exactly what materials and temperature I must use to make one"... that's natural.
B) "Damn, I must learn Japanese to say the proper prayers to the goddess of smithing like those guys do"... that supernatural. It means there is something beyond the natural stuff like materials, temperatures, etc, that can make or break the whole thing.
2. I learn that there is a 5m long Japanese blade somewhere. Which is actually false, since IIRC the Norimitsu Odachi is the longest, and it has a 3.7m long blade, of which actually only about 2.25m long cutting edge and a metre and a half worth of tang. So I'm clearly believing that a sword exists which actually doesn't. Do I think...
A) "Dude, now that must have been a pain in the ass to quench without warping. Hats off to that guy's getting the steel, the temperature and all just right. Mad skillz, that"... that's natural.
B) "Dude, that guy must have been a really holy man, and purified himself and said the prayers just right"... that's supernatural. For the same reasons as before.
(Incidentally for the record, although they did recognize the skill and material quality as important factors, the Japanese themselves did include a hefty dose of supernatural. The ritual parts could go to such extremes as, I kid you not, on the tang of a good quality sword we have an inscription that the smith meditated and ritually purified himself for 100 days before starting to work on it. And, you know, that was actually something to brag about, not a case of "ha, I loafed for 100 days on the client's money.")
3. I notice that when swinging a sword, pushing or drawing in certain ways that obey the pre-existing movement of the sword, result in much easier and faster cuts, while going against this makes it harder, slower and more imprecise. Do I think
A) "There must be a perfectly physical explanation (e.g., momentum), and indeed one can replicate the same effect with just a tree branch or any other object"... that's natural
B) "The sword clearly has its own spirit, who wants to act in certain ways, and for best effects I much act in harmony with the spirit of the sword."... that's supernatural.
(Incidentally the Norse went firmly with option B.)