A fake smile is like a cover for what you really feel. Like putting a mask over your face. When you are really sad and don't want to express your feelings, you would sometimes use a fake smile to stop people from asking if you are alright.

When you think up something brilliantly righteous while baked.

The kind of smile you give when you see someone you strongly dislike (i.e. a raging whore or someone's creepy boyfriend).

A fake smile is best used when around someone you hate. It can also be used to hide how sad you are; This definition is mostly used when in a crowded place (e.g) School, Party, A dinner, ect..