Cider is two things. Hot cider is specifically a spiced apple juice, served hot. Cider also refers to alcoholic cider made from fruits, usual apples. If you go to a bar and ask for a cider in the States you will not receive hot cider.
I think you read that backwards. They're not saying there's no alcoholic cider in America, they're saying it's an American thing to say cider when refering to non-alcoholic apple juice. If you look for cider elsewhere you will get a fruit-based alcohol, you will not get apple juice.
Apple juice is not cider though. Apple juice is clear and flat. Cider (alcoholic) is clear and bubbly. Cider (nonalcoholic) is brown and served hot or cold and spiced or unspiced.
Any of these can be made with other fruit, but apple is the most common.
Interesting, whenever I would make it it would always come out kind of thicker and brownish, especially as it stood around (oxidation I guess). Probably varies by the kind of apple, but the more 'natural' kinds I have found at the store also tend to be pretty brown, certainly not clear.