A fan is someone who likes something because it amuses them and makes them happy. Being a fanatic means that you are a fan to the point that you are obsessed with the thing you are a fan of and you might even try to hurt someone who is not a fan or is a fan of a rival. Or, as the comic above says, is ready for an argument. Take baseball teams, for example. There is a big rivalry between The N.Y. Yankees and The Boston Red Sox as well as between The SF Giants and The L.A. Dodgers. We’ve heard/read the news stories about the “fans” gone wild in the stands and literally hurting someone who was a fan of the other team. I think this is a prime example of someone who has crossed the line from “fan” to “fanatic”. Of course, this is taking it to the extreme. There are also fans of certain musical artists, such as The Beatles, or Justin Bieber. There was the idea that someone was a “Beatlemaniac” and this was someone who loved The Beatles so much they too might be considered a fanatic. I think it might be dependent on what you are a fan of. I am a fan of chocolate, and I know that there are “chocoholics” out there, and I may or may not have claimed to be one, but I would not consider myself a fanatic of chocolate. I might call, say, someone like Willy Wonka a chocolate fanatic. If such a person truly existed. (I am a fan of the original, Gene Wilder version, by the way) I think you get the point I am trying to make here. A fan is someone who likes something. A fanatic is someone who likes something a little too much.
Cake Sharing 
Pingback: Sports teams I like « Having My Cake And Sharing It 2