A fake document is an identity document that wasn't officially produced or recognized. Fake documents can come in different forms, depending on the use case. For example, a fraudster may illegally produce an entirely fake driver's license or Social Security card to use during a loan application process.
Forged documents, on the other hand, are authentic but have alterations. For instance, someone alters a photo or changes the name or birthdate printed on an ID. They can even make an entire document look like a different government agency issued it.