It's different, being made from different plants (original root beer was largely sassafras) but I think the basic formula of root/bark/etc with sweetener is the same.
I alcohol ginger beer? I thought ginger ale.
Definitely a different flavor though, especially most root beer varieties these days which are quite a bit sweeter. Some varieties are made with sarsaparilla instead of sassafras and might be called that instead of root beer, though the name's not really common in the US anymore.
Oh, and we definitely have ginger beer here. I know I've seen Goslings, Bundaberg, Cock n Bull, and Barritts on store shelves at least in the midwest. Plus Crabbies and I think one or 2 others for alcoholic ginger beers.