In 5e Parma Magica is not a supernatural ability. Rather, it's an arcane ability (even though it can only be learned by the Gifted).
As for the reasons why I think Parma is well-designed in ArM5 (in many ways echoing previous posters):
It makes it possible to teach Parma to characters who do not have their Gift "Hermetically" opened. This is what happened in the early history of the Order, and what happens still in House Miscellanea/when new Traditions join the Order. So, a "mechanics-match-fluff" thing, if you wish.
It makes defensive ability more independent of Art specialization, focus etc.
It makes Parma "relatively personal". A magus can extend it to a few favoured people, but at some loss in protection to himself, and only as long as those people remain in relatively close proximity. A Rego Vim Parma would either require rather tricky R/D/T limitations (like the Aegis, but definitely more complicated), or would e.g. be something that a magus can give to mundanes so they can benefit even when away from him etc. It would all get very messy.
And no, Auram or Ignem are definitely not more effective in combat than Rego and/or Vim
What on earth is the difference? I've been a fan of AM for literally decades and I can't keep track of the terminology. Something's really gotta give here if there's ever another edition.
For a game, whose mechanics grow by introducing new virtues/abilities and new ways to get them (see e. g. TMRE and Apprentices), a clean categorization of virtues/abilities from the onset is essential.
At that onset - that's the core rules - it is quite impossible to anticipate every turn, which the further development of the game will take. Hence that categorization tends to be basic and driven by expectations.
The distinction between Arcane and Supernatural abilities is in from the start (ArM5 p.63): Arcane abilities are those every magus will be exposed to and is likely to learn, while Supernatural abilities are self-contained and require their own Virtue.
When HMRE, AM, RM and others later introduced Gifted competitors to Hermetic magi, these competitors are often defined by ability sets containing a mix of Arcane and Supernatural abilities (e. g. PenetrationandSecond Sight). So some readers might no longer distinguish between them properly.
Still, writing for ArM would only get harder with less categories for abilities. AFAICS, RPGs nowadays - like WOIN (woinrpg.com/ ) with its magic system borrowed from Ars - tend to create significantly more.
A Supernatural ability is something that allows you to do ... well, supernatural stuff Like Shapeshifting, Dowsing, and Enchanting others with your music. Unless you are born with a Supernatural ability you can't learn it even if you have a teacher, except under very specific conditions. You need the Gift (and a fairly "unmolded" one) or an Initiation for Magic abilities, and similar conditions for Supernatural abilities associated with other Realms -- every Supernatural ability is tied to a Realm and affected by its Auras etc. etc.).
An Arcane ability is a mundane ability, that everyone can learn -- at least in theory; in practice Arcane Abilities are the stuff known by ... practitioners of arcane stuff like witches and sorcerers, so Arcane Abilities are restricted at character creation very much like Academic abilities, or Martial Abilities -- which anybody can learn, but in practice tend to be restricted to specific social groups. Arcane abilities are abilities like Magic Theory and Lore, but also Finesse and Penetration, that give you a better understanding of supernatural stuff and by that token allow you to do more with supernatural gifts you already possess (including e.g. magic items), but generally lack much "oomph" when used on their own.
Personally, I think that the distinction between Academic, Martial, Arcane and General "mundane" abilities -- and Supernatural abilities -- is no big deal, and in fact it makes thinking about Ars Magica characters rather easier. As OneShot noted, it's one of the very very basic things in the ArM5 corebook, nicely explained on p.63.
Ok, granted I should have remember that one. I tend to think internally of these skills as hermetic rather than arcane abilities, probably because the game has hermetic (vs. supernatural) virtues. Nonetheless the terminology is overly complex, particularly when a single skill can be arcane or supernatural to different practitioners and a virtue can vary between hermetic or supernatural in the same way, and perhaps also be a mystery virtue at the same time.
For all that, Parma Magica remains a rara avis so the usefulness of all this categorization is questionable.
Hmm. I think that the comparison with Hermetic and Supernatural Virtues is a bit confusing; in particular, I think that the division between Hermetic and Supernatural Virtues is a bit confusing, or rather becomes confusing once you start playing Hedge Wizards. That's because Hermetic Virtues (and Flaws) cover both stuff that in the corebook only magi could have because it was related to their magic -- like a Magical Focus or Twilight Prone -- and stuff that in the corebook only magi could take because it was related to the Order's social "organization", like Hermetic Prestige. The former can be taken, with the appropriate changes, by non-Hermetic magicians; the latter can be taken only by members of the Order, including unGifted ones like Redcaps.
This division between supernatural stuff that one can learn only if one has a talent for magic (even without outside training), and mundane stuff that anyone could learn but is in general taught only to folks that have "arcane careers", is what the division between supernatural and arcane abilities is all about. I really, really do not find it confusing at all.
When you think of it that way the distinction makes sense - but Parma Magica doesn't fit the definition of an arcane ability as "mundane stuff that anyone could learn" at all.
Parma Magica indeed appears to be an exception, but it's very handy to place it into arcane abilities because the mechanics of arcane abilities are perfect to handle Parma with the single twist that one must be Gifted.
That said, maybe Parma is not as much an exception as it appears to be. Maybe there is something intrinsic in having the Gift -- akin to having Magic Might -- that grants Magic Resistance if you learn how to exploit it. And Parma Magica is indeed this "mundane" understanding of your Gift, that is nonetheless necessary to get Magic Resistance out of it in the same way that Magic Theory is necessary to create invested devices (because without Magic Theory, you can't handle vis).
