The way I see it, there's three classes of Legendary Pokemon, all under the general umbrella of "Legendary." There's Sublegendary, Legendary, and Mythical.
Sublegendaries aren't technically Legendary in the game code, and they're just powerful Pokemon with a specific powerful ability. Often there's no guarantee they're on of a kind, they're never banned from official tourneys, and they have green entries in Gen 7. They're essentially just "special, unusual, or especially important or powerful Pokemon."
Legendaries cover most others, including all boxart Legendaries, Zygarde, Mewtwo. There's only one of each of these (except Solgaleo/Lunala/etc) because they're unique forces of nature that control reality as we see it. They're usually banned from tourneys, and many of them are Uber in Smogon as well. Their Pokedex entries are gold. They're "one of a kind, forces of nature that can grant people inhumane levels of power over reality." These are usually the Pokemon the villains want.
Finally, Mythicals, which are also gold in the Pokedex. They're a special rare subclass that is more or less defined by not being available ingame. Deoxys is, of course, an exception, but Mythicals almost always have to be recieved or obtained via item.
In my opinion, the subclasses only exist for gameplay categorization, to categorize legendaries into groups as such: "Lesser/less OP, Greater/Usually OP, and Rare/Event-only."
I don't mind if other people have other definitions, but this is the closest to what the game data actually uses, and the fact of the matter is it's mostly for the game's sake, and we're free to categorize them however we like.
