I think there’s two terms: Mafia and mafia.

mafia - generic catch-all phrase for organized crime groups. Used as a simple, short way to describe a group of criminals, however loosely structured.

Mafia - as in “The Mafia” means specific Italian groups that have strict rules and formal membership and structures.

Meaning there may be “Russian mafia” but they won’t be recognized as equal members or peers by the Sicilian Mafia by other made members in Sicily. Whereas the Sicilian Mafia would recognize members of the Camorra, even if their organization names and structure are slightly different.