Sorry, in greek those terms tend to mean the same...
Btw, 'classic' is ultimately derived by the classes system in the 5th century bc (iirc), and started being used as a synecdoche for anything golden-era like
classic and high literature are vastly different. classics are classics because of a (scholarly or not) consensus, because of their longevity and because many feel they convey a subject matter (a tale, a phenomenon, or such) that is timeless and always relevant.
high literature may be completely obscure, not recognized, not relatable at all, it's basically anything that is intellectually challenging, complex, insanely well-crafted and has a certain edge (of madness or grandeur) to it.
the odyssee is a classic, zettel's dream is high literature, for example
just my 2ct
There is this quote, attributed to Oscar Wilde, that says there's only two kinds of literature: good litersture, and bad literature. Whether it is high(brow) or not has little to do with it.
At this point we can say that classic is the same as canonic: a corpus that academia has deemed worth talking about. Much of it is good, much of it is bad, much of it has been forgotten in time and much more has been purposefully excluded from it.
It is a useful category insofar as these are most usually well-written, but it is worthless as a category to help determine your taste.
I think that's dumb, there is no "de facto" good or bad lit, just lit with different ambitions (noble or selfish) and different levels of craftsmanship, which is already bordering on arbitrary territory (from brute to master or something). so, say a 50 shades of grey has the amibition of arousing the reader and making bank, and isn't very well crafted. whether or not it is bad or good art still cannot be judged objectively.
"high brow" - what does this really refer to? it's honestly more about subject matter, aesthetic and discourse than it is about the writing itself. high brow could be joyce's letters to Nora about fart sniffing - the subject is edgy and controversial enough, the prose is weird enough, the discourse (sexuality, power dynamics, deviation, fetishism) is contemporary and hip enough. most importantly, "high brow" says little about substance, it's mostly a stylistic description imo.
I 100% agree that classic is the same as canonic, that is pretty much the definition