Crime "families" tend to be associated more directly with their respective territories than the individuals to whom their members may or may not be related.
In the Sicilian language, the word cosca, which is the crown of spiny, closely folded leaves on plants such as the artichoke or the thistle, symbolizes the tightness of relationships between members.
As the Mafia was imported into the United States in the late 19th century, the English translation of the word cosca was more at clan or family.
It can further be speculated that the Mafia was simply emulating, to a certain degree, a more medieval order in which a noble family would more or less serve as the power in a local village, in a sort of inverted hacienda culture.
Nevertheless, the term stuck, both in the minds of popular culture as well as the national law enforcement community, and eventually began to be used to describe individual units of not only Sicilian gangsters, but those whose origins lie in other parts of Italy (e.g., the aforementioned 'Ndrangheta, the Neapolitan Camorra, the Apulian Sacra Corona Unita, etc.).