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GhostQueen13 (I hope Doe doesn't mind me barging in, I saw it because I'm subbed to the thread), I'll explain what I know but do make sure you ask someone who actually is one of these when you see them!
Sapphic/wlw (women loving women) is a reference to sappho, a female greek philosopher from the island of lesbos (where the word lesbian comes from) who wrote poems about how beautiful women were. I guess some people just prefer to use sapphic in place for lesbian, but I don't know of any actual difference.
Acchilean/mlm (men loving men) is actually one I didn't know about, but I can gather it's just a variation of the sapphic flag for gay men referencing acchiles. Will definitely look it up though!
The Sappho Lesbian flag is also just a variation from the lesbian flag (like the lipstick lesbian, the full pink shades and the orange pink). If I remember correctly there's people who prefer this flag because of the story behind the other ones and/or the meaning of the colors.
As for queer, the original meaning of the word is "weird". It came to be as a sort of insult for people who deviated from the norm, used quite some time ago for anyone LGBTQI+. The movement took that word and used it with pride, like (yeah I'm queer, so what?) and the word became an umbrella term for LGBT+ folks. If you don't think you fit in any category, or just don't wanna put yourself into a box, but you know you're not exactly straight/cisgender/etc, you can define yourself as queer!
Genderqueer, too, is a way some people who feel that they aren't cisgender can define themselves without specifying what, exactly, their gender is. Maybe they don't want to fit in a gender box or just vary a lot, there's many reasons.
Finally, xenogender is someone who doesn't want to be defined by any genders or anything in the gender spectrum. Like they're their own kind of gender.
I hope this helps! If anyone else wants to correct me feel free to!