Hm! I've always defined this differently. Supernatural stuff wouldn't be affected by dispel magic, for example. Magic effects—even if not spells—would be. And spells are what have components and cast times and levels and (usually) slots, and can be counterspelled.
Sure, that's basically the 3e way, but being fast and loose with the line between (Su) and (Sp). But you're still bringing in a ton of
spell baggage here: things subject to the
spell dispel magic, or to the
spell antimagic field, etc.
I'm using the term "supernatural" in its ordinary sense: that which is beyond the limits of the natural. I include in this category things I call "transmundane": stuff that isn't magic or spells or any of that faffery, stuff that theoretically arises from superlative mundane skill, but which exceeds the limits of what "ordinary" things should be able to achieve.
The transmundane and non-magic supernatural power are horrifically neglected in 5e as it currently stands. I mean, for God's sake, it is an outright spell, a
third-level spell, to be able to shoot lots of arrows at once (
conjure barrage, or its FIFTH-level counterpart,
conjure volley). I want a world where a blacksmith does not also need to graduate from a magic academy or have a dragon (and/or deity) in the family tree in order to make weapons with supernatural properties. I want a world where encouraging words, if spoken persuasively enough, truly can draw out the inner reserves a person never knew they had. Where a rogue whose skill grows from excellent to world-renowned to legendary can start doing things that shouldn't be physically possible, but somehow, still happen, like stealing the color of a maiden's eyes or a memory of an important event. Where the unyielding faith, stalwart and true, of a single person can be more than just a
metaphorical light in the darkness, but actually turn back the night.
Because a world where those things happen is one that still feels "magical," even though none of those actions is Magic, the official D&D game mechanic by that name.