I may expand the question adding "fake" and "phony" but "false" and "fabricated" just don't seem to be fitting in.
But I think they are all synonyms excluding false and fabricated, but there may be some differences such as being a criminal act or not. ( "Fake" sometimes refers to a criminal act such as a fake id but sometimes not (such as fake fangs) )
I've mostly heard bogus, phony and forged in the context of a specific criminal act;forgery
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