Some context : This trope is named after characters from Archie Comics, wherein the main character ("Archie") is caught between two love interests with drastically different personalities. "Betty" is the sweet, reliable, everyday Girl Next Door type (which could mean "kind of dull"), while "Veronica" is more alluring, exotic, and edgy, but has more of a mischievous or icy personality (which could mean "kind of a bitch"). This translates to their physical appearances; Betty will be pretty but modest in dress, while Veronica will be Ms. Fan service in all her glory. And this also mean they all have different colored hair as per the Blonde, Brunette, Redhead trope.
Betty and Archie are loyal comrades and usually best friends, with Betty secretly pining for him while he (unaware of her feelings) is attracted only to Veronica, the sultry Ms. Unattainable who barely notices him. Betty, who wants Archie to be happy, may assist him in his pursuit of Veronica, even though we all know how much she wants him for herself. Another possibility is that Archie and Betty are already in a relationship, but then Veronica starts batting her eyelashes at Archie and causes friction between the couple."Archie," "Betty," and "Veronica" can be any gender or orientation It's probably the dumbest of love triangles due to this being the main plot line in so many teen dramas...Looking at you Hetalia.
Ordinary High School GirlKagome is the Betty and Dark Magical Girl Kikyo the Veronica, in Inuyasha Solved when Kikyo dies for a second time but now is able to go in peace, so Inuyasha finally lets go of his regrets and stays with Kagome.
X-Men had a long-running Love Triangle with Jean Grey, Cyclops (Betty), and Wolverine (Veronica)...which was turned on its head during Grant Morrison's early 2000s run, which introduced a Betty And Veronica love triangle with Cyclops as the center figure, Jean as the Betty, and Emma Frost as the Veronica. Then Jean dies, with the writers claiming she won't be back, but literally no one believes this so... take it with a grain of salt.
Beauty and the Beast gives us the Beast as the Betty and Gaston as the Veronica to Belle's Archie. But this is Disney we're talking about, so...
Deltora Quest has the genderflipped version with the straightlaced, dependable Lief (Betty) and the exotic-but-beautiful Dain (Veronica) for Jasmine's Archie.
Applies to Danny Phantom, where Danny is infatuated with Paulina, the shallow, beautiful "Veronica" of the school, ignoring the pretty, intelligent "Betty" at his side, Samantha Manson. The love triangle isn't clear at the beginning of the show, when Samantha and Danny are Just Friends, but eventually their feelings do grow for each other.
Please avoid referring to characters as "the Betty" and "the Veronica" to someone else's "Archie" when referencing this trope. It is not particularly helpful to those tropers who are not familiar enough with the characters in question to immediately extrapolate the implied relationships. If anything this is the "Rich Suiter, Poor Suiter" but the love triangle most definitely involves friends.