Here’s how a 1921 magazine article described the different types of ice cream:
Classes of Ice Cream
There are three distinct classes of Ice Cream: The Philadelphia, which is supposed to be made of heavy cream; the French, which is made with eggs on a soft custard foundation; and the so-called American, which is made on the foundation of a thin white sauce. All three classes are made in New York, and in every other large city, but we have never heard that any special recipe for ice cream is peculiar to New York. The less expensive form of cream, in that and every other city, are those based on a thin white sauce, sweetened sauce, sweetened, flavored, and frozen.
American Cookery (November, 1921)