You're on the right track pal. Clemenza in the Godfather is a capo or captain of the Corleone Family. Paulie is the same rank in the real life Lucchese Family. Paulie controls a crew of guys in the Mafia known as Made Men. These are the Italians and if you remember Henry says he can't ever be a made man because his father was Irish. So Henry's official rank is an associate of the Lucchese Crime Family. He hung around with Jimmy's crew which were made up of Irish, Italian and I think one of them was even hispanic. This crew were basically all associates to Paulie's crew.