For ATL<->SFO the directs are Delta, Frontier, and United:

Frontier doesn't have a business class nor long haul international flights (they are an ultra-low cost carrier).

Delta calls their highest tier "Delta One" their business class offering. It's mostly available in mid & long haul international flights, though there are a few select domestic routes with it IIRC. A tier below is First, which is available for both domestic and international flights. https://en.wikipedia.org/wiki/Delta_Air_Lines#Cabin:~:text=D...

United's highest is called "Polaris", representing their international business class. Confusingly, they have "United First and United Business" as the next class. I.e. it's the same class but on domestic flights they call it "United First" and on international flights the same seat would be sold as "United Business" despite having Polaris for that already. Regardless of that oddity, the First class can't be higher than itself named Business class even compared directly instead of with the actual business class Polaris - it's the same seat. https://en.wikipedia.org/wiki/United_Airlines#Cabins:~:text=....

Other airlines label and order things differently of course. E.g. American has Flagship First above Flagship Business above First/Business (shared much like United on that 3rd class) and maybe that's where your experience is. To my knowledge though, no such airlines operate the ATL<->SFO route originally described though.