Fake is used to describe something not made by the original manufacturer or origin. A fake diamond or a fake dollar bill. Artificial is used to imply "man made" or not using original parts. An artificial lung, artificial sugar. Artificial flavor in your coffee. False is a term used to describe a lie or something misleading. A false statement is untrue. A false door is a door that doesn’t open. Imitative is a term to describe when something is made to look like another or behave like another. His behavior is imitative of his father = He wants to behave like his father. In America, we rarely use this term

This is a good question. I would like to know too. Artificial or imitative seems easier, but fake and false looks like the same.