Fairy tales come from oral traditions and the stories are hundreds of years old. Modern fantasy stories have authors that wrote from their own imagination but may have borrowed elements from fairy tales.

A book of fairy tales would typically be classified as fantasy literature. This genre encompasses stories with magical or supernatural elements, often set in imaginary worlds.

Frances Diane Neal has written:

'Fairy tales for grown-ups' -- subject(s): Fairy tales, Women and literature, Fairy tales in literature, History and criticism, Criticism and interpretation, History

...fantasy stories.

any fantasy novel will have a fantasy setting, normally it will be fairy tales or mythical type books