Forgotten Realms is actually a campaign setting. Baldur's Gate and Icewind Dale are both in the FR campaign setting.

D&D can take place in FR, but it's not exclusive to it. Another popular campaign setting is Eberron. Living Greyhawk is another. They're not worlds but universes, as different campaign settings can have different deities, planes of existence, etc.

And finally, there are a lot of books set in the Forgotten Realms setting, so it's sort of a book... if you wanted to say that.

What is it they say about silence being golden?