Folktales, Fairytales and Fables?

I'm doing a study on anthropomorphism in 19th and 20th century Children's Literature and I’m noticing fairytale, folktale and fable being used interchangeably, especially when mentioning Aesop’s writings. In Children’s Literature I see they all fall on common grounds; that they provide a witty way of offering moral lessons but I think that folktales and fables have a more realistic theme as oppose to the mystical theme usually found in the fairytale genre.

I’m looking for sources that can demonstrate their differences or are they so similar that it is fine to use them interchangeably??