Ever hear of a dictionary? They have different definitions, and the definitions for fake and false are not the same, and 'fake news' has a specific definition of its own that precludes merely mistaken or biased news.
As for synonyms, a synonym for 'boat' is 'yacht', that does not mean that my boat is a yacht.
As for synonyms, a synonym for 'boat' is 'yacht', that does not mean that my boat is a yacht.
I'm not anti-Christian. I'm anti-stupid.