The difference between the mob in the historical sense of the word, and a gang, was how they exerted influence.

Both have territories. Both bully people. But the mob used corrupted official institutions to influence others. Gangs just threatened physical violence. Before someone says that mob enforcers also threaten physical violence and extort people, you have to remember that the root of their extortionist power is corrupt police and judges.

So a gang will threaten to beat you up, but the mob will tell you they can beat you up if they want to and no one will protect you because the local cops and FBI are on the mob payroll, so pay up. And if you try to go to a cop or a fed and we find out, you will pay. We have informants.

The same theory extends to intra gang and inra mob affairs. In a gang, the strongest rule the weakest. It is a physical pecking order. In the mob, the most connected rule those less connected. The ones with the judges, cops, money, hitmen, etc, rule over their lessers, in the mob.