Crews are small working groups that work on specific jobs. A caporegime heads a regime that contains soldiers, who may be called upon to do different jobs at any given time. They form themselves into crews to carry out those jobs. Some jobs are carried out at the behest of their caporegime, or with his blessing. Crew heads can pull jobs on their own, as long as they stay within the pre-arranged groundrules, one of which is to pay a tribute to the caporegime out of the proceeds of any independent endeavor.

Remember that in GF One, Sonny tells Tom Hagen that the family has 100 buttonmen on the streets 24-7, so if Solozzo shows even a hair in his ass he gets whacked. What happened was that the caporegimes pooled all their crews together for the war against the Tattaglias and Solozzo, under Sonny's orders.