To me, apple juice is what you get when you squash apples, and cider is what you get when you ferment apple juice. There is no such thing as non-alcoholic cider.
From watching an episode of the Simpsons (when Flanders has a rhyme to remember which is apple juice and which is cider) and an episode of Alias (where one of the characers says she wanted to buy wine, but got carded, so had to buy cider) I gather that cider is a non-alcoholic drink in the USA.
What is it? How does it differ from apple juice? What do you call the alcoholic beverage made from apples?