It really depends on the situation. Sometimes, fake and false can be used interchangeably and that completely depends on the situation. Sometimes they cannot be used interchangeably. Most of the time, they CANNOT be used interchangeably because they mean two different things. For example: You have given false information. You have given fake information. Those two sentences above CANNOT be used interchangeably. The correct way to say it would be, "You have given false information." That means the information is not true, wrong, incorrect, not factual. Fake means it's artificial, not genuine, a copy or imitation. Like the guy said above me: "That Gucci bag is fake." That means it's a copy or imitation or counterfeit. It's not a real Gucci but an imitation of one. Hope this helps!

That Gucci bag is fake. You have a false idea about how people live in this country. Sometimes in certain situations they might be interchangeable. a fake/false laugh for example

As adjectives the difference between false and fake is that false is untrue, not factual, factually incorrect while fake is not real; false, fraudulent. As a adverb false is not truly; not honestly; falsely. As a noun fake is something which is not genuine, or is presented fraudulently or fake can be (nautical) one of the circles or windings of a cable or hawser, as it lies in a coil; a single turn or coil. As a verb fake is to cheat; to swindle; to steal; to rob or fake can be (nautical) to coil (a rope, line, or hawser), by winding alternately in opposite directions, in layers usually of zigzag or figure of eight form, to prevent twisting when running out.

I prefer to see this difference in usage [instead of telling what it should be]. "false" is "untrue", usually according to evidences. That can be by mistakes or ignorance. "fake" is also "untrue" but intentional. That intentionality can bring up "untrue" meanings by messages of "true" contents as well. Hence, "fakes" is about the meaning but "false" is about contents.