In what's still an Italian-American neighborhood of Williamsburg, Brooklyn, there used to be a stand (shown below in decay, and since vanished) whose wares included both cream ices and water ices, as well as ice creams and shakes. I understand that "water ice" is often considered a synonym for "Italian ice." Nowadays, is "cream ice" more commonly known by another name? Is it simply an Italian ice prepared with a certain amount of dairy?
Put plainly: Would some Chowhound explain the distinction between cream ices and water ices? Thanks in advance.