Cosa Nostra vs crime syndicate

Cosa Nostra and crime syndicate both are nouns.

Word	Noun	Adjective	Verb	Adverb
Cosa Nostra	Yes	No	No	No
crime syndicate	Yes	No	No	No

As nouns, crime syndicate is a hypernym of Cosa Nostra; that is, crime syndicate is a word with a broader meaning than Cosa Nostra:

Cosa Nostra: a crime syndicate in the United States; organized in families; believed to have important relations to the Sicilian Mafia
crime syndicate: a loose affiliation of gangsters in charge of organized criminal activities

Other hypernyms of Cosa Nostra include family, mob, syndicate.

Cosa Nostra (noun)	crime syndicate (noun)
a crime syndicate in the United States; organized in families; believed to have important relations to the Sicilian Mafia	a loose affiliation of gangsters in charge of organized criminal activities