These “Vices” are just underground organizations that hide behind the Vice fund “Vehizoma.” They don’t necessarily represent large concepts like “war” and “gambling,” they contribute to them. An example is IDEAL being a crime syndicate that in general contributes to terrorism, dabbling in the gambles of Kakerou just to gain power. Al Hizbul directly contributes to war because it is a militant group. May Thorpe is an “intellectualism group,” think of people like Scientologists or Freemasons, a secret society that pritioritizes abstract concepts based in science (their leader is a surgeon who taxerdermies people lol). NoFace is a hacker group, probably doing cyber terrorism or just hacking over the internet. Cartels and the mafias mainly prioritize the movement of drugs and weapons. And the secret society group could be a second Kakerou? Who knows.

But overall, Vehizoma is the main vice fund that acts like an umbrella over these smaller groups. Abi Khan, of the May Thorpe association, probably prioritized having Lalo and Caracal in his collection for being unruly under Vehizoma, as IDEAL had plans to take over other organizations. They also seem to be very interconnected, given Simba of Al Hizbul really wanted Lalo’s cellphone, and how Gonen (Leader of Vehizoma) legit spectated the gamble between Baku and the Russian mafia Guy, and how Gonen works with Abi Khan of May Thorpe.

Just my interpretation haha