A real fan usually has been a fan for a long time, and likes other bands similar to them such as P!ATD, Green Day, My Chemical Romance, etc. and likes songs other than songs from the Save Rock and Roll album.
A fake fan usually is a fan of mainstream/pop music and discovered Fall Out Boy from the radio, when it played "My Songs Know What You Did In The Dark (Light Em' Up). That is basically the only song they know. They label the band as emo, even though they are clearly not.
Fake Fan: <3 omgggg I luv da Fall Out Boys! Light Em' Up is my fav songgg!!! Oh and I think his name is Pete Stump but he is rally hoooottttt <3333 I am like sooo über emoooo!!! lol I'm so hardcoreeee ^_^
Real Fan: I fucking love Fall Out Boy. Joe is my favorite because of his cool Afro! From Under The Cork Tree is such a cool album, but Save Rock and Roll was ok, I was expecting more tho. I miss Patrick's sideburns and Pete's guy liner +_+. And if you label them as emo, you die.