

That’s not the difference. Both words have noun and verb forms.
Immigrate = to move to a place
Emigrate = to move from a place
Immigrant = a person who moved to a place
Emigrant = a person who moved from a place
So they would be emigrating from the US and immigrating to Italy. They would be a US emigrant and an Italian immigrant.
Right movie, wrong character. Gus Gorman, played by Richard Pryor, skimmed the money from discount Gene Hackman (Ross Webster, played by Robert Vaughn).