My Organized Crime professor described it exactly the way that Boss_of_bosses did, except that he switched Capo Crimini and Capo de Tutti Capi.

He described it as Capo Crimini (often referred to as simply "Capo") is the Don, or the Godfather, of the family.

The Capo de Tutti Capi, meanwhile, is the Boss of all Bosses. He is the main guy over all of the families.

The Capo de Capi is a very hard position to attain because Bosses don't like being told that they have to report to another Boss.

The first declared Capo de Tutti Capi was Salvatore Maranzano after he won the Castellammarese War. Even though he declared himself Capo de Capi, he really didn't last long enough to earn the title and was soon killed by Charles "Lucky" Lucciano, who became the first real Boss of Bosses.

Lucciano was successful because he never actually declared himself as the Capo de Capi. But he was pretty much recognized as the man in Organized Crime after defeating Maranzano and establishing the Commission, also known as La Cosa Nostra.