Actually, I don't get the impression anyone really knows much about the Ajahs. Aes Sedai especially seem to be more inclined to quell any though of an outsider judging or making distinctions among the sisters: as far as anyone else is concerned, they are ALL Aes Sedai, and that's all anyone needs to know. They don't WANT people favoring one Ajah or another, or judging any sister by any criteria other than possession of shawl and ring. Until the Wondergirls start getting deeper into their training, even the readers don't know much about the differences. We had no idea what the Greens were all about, or why they had so many Warders, until Egwene asked Alanna in tDR (something she and Elayne both failed to pick up throughout their entire novitiate). That said, fighting supernatural threats DOES seem to be the most obvious notions to occur to people signing up for such an organization, even if they don't know exactly who does it. We would have thought Auror was a cool job in the Potterverse even if we never knew there was a word for it.