That's what my mother told me what class we were flying when I was a child internationally. She told me that business/executive class was called "second class." I never heard such references from anyone else.
Now she refers to the "main cabin" "as cattle class". My dad calls it "chan kwai". (In Thai, chan means "level", aka "class". "Kwai" is a water buffalo. Cattle isn't common in Thailand, but they get the same idea using water buffalos instead of cattle.)
I think "third class" should be resurrected!

Enough with "main cabin", "coach class", "tourist class", "world traveler".