This is mainly a Japanese Media Trope but does occur occasionally in other media. Two girls have largely different personalities that both lie on the traditional masculine spectrum.
This has a tendency to happen in an Improbably Female Cast where varying male personalities are limited and in Yuri to give the lesbians and the audience one more androgynous girl to drool over. This usually takes the form of one girl being a lad-ette personality-wise and the other girl will be a more refined Prince Charming complete with a Bishie Sparkle. Other variations exist as well, such as the likelihood that one may be more athletic while the other one is a Badass Bookworm.
As with any two-character trope, the two characters have to have some sort of relationship with each other, be it friends, family, love interests, or rivals for a love interest, so the two characters can be playing the traits directly off each other. Expect a Pseudo-Romantic Friendship if it's a Yuri. Expect an Odd Friendship regardless. Sometimes the girls will not get along and there will be moments of rivalry or even Belligerent Sexual Tension between the two.
Compare the Bifauxnen to the admirable one and the Lad-ette to the mannish one in Four-Girl Ensemble and compare both to the tomboy in Tomboy and Girly Girl.
Contrast the polar opposites, Light Feminine and Dark Feminine — two girls who are both feminine, but in different ways — and Noble Male, Roguish Male — two guys who are both masculine, but in different ways.
- In Ai Ore! Love Me! Considering almost all of the members of the band Blaue Rosen are girls that fit either the Bifauxnen or Ladette aesthetic or both, this trope is a given.
- Sylia Stingray and Priss Asagiri in the Bubblegum Crisis OVA. They're more of a Tomboy and Girly Girl deal in Tokyo 2040, however.
- In Hellsing, Integra Hellsing, Rip Van Winkle and Zorin Blitz are all masculine women with distinct and opposing personalities.
- In Monthly Girls' Nozaki-kun, we have Yu Kashima as the Prince Charming Bifauxnen and her "singing coach" Yuzuki Seo as the foul-mouthed and abrasive ladette. As Seo does not actually look masculine, they were once mistaken as a couple when seen hanging out together by Wakamatsu who assumed that Kashima was a boy.
- Pictured above: Kaoru Orihara (brunette, on the right) and Rei Asaka (blonde, on the left) in Dear Brother, arguably the archetypal examples. Rei is a stoic depressed loner that sometimes gets mistaken for a man and talented basketball player and artist; Kaoru is an extremely androgynous Lad-ette that is just as good in basketball as Rei is, not to mention she's arguably the only sane person in the story. While they are both athletes, Kaoru takes basketball much more seriously than Rei, who is too doped up to care much about anything, though when she does play, it seems to be the only healthy source of enjoyment she has. Coincidentally, that happens when Kaoru is having a relapse in her illness and Rei takes her place to help the team. Also alluded to in their "titles". Rei is called "Hana no St. Juste" which means "St. Juste of the Flowers", while Kaoru is called "Kaoru no Kimi" aka "Prince Kaoru".
- PriPara: Hibiki plays the Bifauxnen of this dynamic with both Shion and Dorothy.
- In Sailor Moon, Haruka Tenoh and her rival Seiya Kou play the trope straight in the manga but only plays with it in the first anime considering that Seiya is a Gender Bender in it. (So she only played it straight in her Sailor Starfighter identity, which is the original one.)
- Handsome Girl And Sheltered Girl features (as the name implies) a Bifauxnen and a Girly Girl (who thinks the first is a guy for quite some time but stays with her after finding out). They get a Relationship Upgrade later where the "sheltered" girl turns out to be much more assertive when drunk, fitting The Lad-ette part more.
- Puella Magi Madoka Magica: Sayaka and Kyouko. Additionally, the two clash a lot and have a Belligerent Sexual Tension due to their rivalry and opposing ideals (idealism versus cynicism, also respectively). Sayaka is the more androgynous among the Puellas and she displays typically tomboy traits such as being into sports, wearing her hair short, and not fearing getting physical to protect her friends (mostly Madoka). Moreover, she is very chivalrous and justice-oriented. If that's not enough to qualify as a (downplayed) Bifauxnen, remember her Puella Magi suit is modeled after a Knight in Shining Armor with a cape and swords. Kyouko, on her part, is a very outspoken, roguish, and cynical girl that lives in the streets. She even has a sadistic streak and her pattern of speech reflects her aggressivity and brashness. Her Puella Magi suit, in turn, has her wielding a fragmentable spear connected by chains. And she also loves eating. All in all, she's a Lad-ette.
- Wonder Woman (1987): Cassie is a teen with Boyish Short Hair and a spunky attitude who wears loose baggy clothes and is easily mistaken for a boy while fitting the visuals of an attractive teen boy for her time period, while her best friend George is more intentionally androgynous and has a more delicate and traditionally attractive appearance.
- X-Wing Rogue Squadron: Plourr Ilo is the gleeful, bloodthirsty Boisterous Bruiser who loves to tease her friends and tends to take charge; she's also secretly a princess. Xarcce Huwla is soft-spoken, cultured, possesses an understated sense of humor, and is restrained. They're both big and muscular and proud of their fighting skills, and Xarcce's species has little sexual dimorphism, and they both play The Big Guy at need. The two are shown having a friendly sparring match, with padding, and then go drinking together.
- Chronicles of the Kencyrath: Jame (the protagonist) and Brier Iron-thorn (her Number Two). Both are androgynous badasses, but they're still quite different from each other. Brier is The Stoic, very military and highly disciplined, and Jame is… kind of a loose cannon and a Walking Disaster Area Anti-Hero. They have a Red Oni, Blue Oni thing going on, and stern Brier is the Conscience to Jame. Physically they contrast too, though both are Bifauxnens. Brier is tall and sturdy, with Boyish Short Hair, and Jame very skinny and waif-like, with long hair.
- In Strawberry Panic! Amane Ohtori plays this role opposite Kaname Kenjo.
- A western lesbian example can be in The L Word:
- Shane and Carmen: Shane is a famously androgynous-looking alpha-lesbian. As a young abandoned orphan, she used to make a living as a prostitute, working with gay, male clients. Personality-wise, she can be seen as a gay female take on The Casanova. She is very charming and suave. Her girlfriend, and later fiance Carmen, is a tomboyish Hard-Drinking Party Girl of the Spicy Latina variation, who works as a DJ. She is blunt and very energetic. They make somewhat of a Red Oni, Blue Oni pairing.
- The show also features a non-romantic example: Tasha — The Squadette, who gets very Biaxfunen in her National Guard uniform — and her BFF, Papi — The Lad-ette. Personality-wise, this pairing plays this trope pretty straight. Tasha is very quiet and has surprisingly traditional values — which are often lampshaded. She enjoys treating her love interests like an old-fashioned male suitor would. Papi, another Spicy Latina, is a total player, and a very clear example of The Lad-ette. She plays high-stakes poker and basketball, drinks a lot, and even outshines Shane in the field of random hookups.
- Star Trek: Deep Space Nine: Jadzia Dax is a cool, suave, worldly, Ace Pilot with several lifetimes of experience behind her. Kira is a grizzled ex-resistance fighter wrestling with her home planet's tragic past and uncertain future. There's no tension between them, sexual or otherwise, just friendship and advice.
- Dragon Age: Inquisition: Sera and any androgynous-appearing female Inquisitors from Sera is crude and boyish, telling her friends rude stories and reveling in playing pranks, while the Inquisitor can be much more reserved and severe. Even if they're dating each other (which may prompt the Inquisitor to get involved in Sera's antics), the Inquisitor's dialogue generally has her be a lot more level-headed and polite.
- Paragon Femshep from Mass Effect has this dynamic with Jack. Paragon Shepard is composed and diplomatic. Jack is violent and snide.
- In Pokémon GO, Blanche of Team Mystic is a woman who dresses well in an androgynous fashion (along with her ponytail), and acts in a more analytical tone. Candela of Team Valor has shorter hair and lean body with ample bust, and relies on strength, but is easily enamored by the small, cute Pokémon.
- Steven Universe:
- The core Crystal Gems exhibit a three-person version of this dynamic. Amethyst is the Ladette, being a crude and playful tomboyish "rebellious teenager" type (despite being thousands of years old), whereas Garnet and Pearl exhibit the Bifauxnen aspect in different ways, with Garnet expressing the mature and composed Team Dad-style leader side, while Pearl is a tender Team Mom who exhibits the traditional elegant "otokoyaku" aesthetic.
- Of the first three Homeworld Gems shown, Jasper and Peridot likewise contrast from the very feminine Lapis Lazuli in different ways. Jasper is an enormous, muscular, hyper-aggressive Blood Knight. Peridot is small, technology-inclined, and tries to handle things analytically. Both wear jumpsuits, in contrast to Lapis' dress.