With the "Anomina Sarda" they probably mean the various, mostly individually working robbers and kidnappers that come from Sardinia. Sardinia doesn't even really have any gang-like organized crime groups, let alone some kind of "mafia". Individual criminals, sure, but nothing of a long term cooperative criminal gang.

Corsica is extremely close to Sardinia. Both islands have their differences, but also many similarities. The tribe the population supposedly descended from, the Corsi, are actually native to Northern Sardinia and probably were a Sardinian tribe. Corsica throughout history has also had a large influx of people from Liguria. In general I would say Corsicans are closer to Italians than they are to French people, but they would probably describe themselves as just "Corsicans" first and foremost.

I'm not extremely well-versed on the "Corsican mafia", but from what I read I think they're more structured like the Camorra: into different clans or gangs consisting of criminals that come from the same area. The Bastia area for instance had the "Brise de Mer" gang that was named after the bar where most of the members frequently met, as Martial already stated a few posts above.