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.

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..