To my mind there are two major types of fantasy: fantasy that takes place on some version of Earth OR fantasy that takes place on a so-called "secondary", i.e. made-up imaginary, world. This second type of fantasy is often called high or epic, sometimes it's called heroic or medieval fantasy or sword and sorcery fantasy. The quintessential author here is J.R.R.Tolkien, with George R.R. Martin also hugely successful. Epic or high fantasies often involve a quest, so sometimes are called quest fantasy.
Bridging the gap between these two types of fantasy are fantasies involving a portal. Often the portal goes from Earth to the secondary world. C.S. Lewis' Chronicles of Narnia are a great example of this.
Back on Earth (also called the primary world), we can have superhero fiction or historical fantasy or weird fiction or science fantasy or insert_your_favorite_here.
What about fairytale fiction? It could occur on the primary world or a secondary world, so this one depends on the story.
Have I confused you? Sorry. The bottom line here at Electric Spec is we don't care what sub-genre your story is. Just send it in!