Folklore is the traditional art, literature, knowledge, and practice that is disseminated largely through oral communication and behavioral example. Every group with a sense of its own identity shares, as a central part of that identity, folk traditions–the things that people traditionally believe (planting practices, family traditions, and other elements of worldview), do (dance, make music, sew clothing), know (how to build an irrigation dam, how to nurse an ailment, how to prepare barbecue), make (architecture, art, craft), and say (personal experience stories, riddles, song lyrics). As these examples indicate, in most instances there is no hard-and-fast separation of these categories. https://www.afsnet.org/page/WhatIsFolklore 

This page will concentrate on different kinds of folk stories.

Folk Tales and Legends are genres of folklore that consists of a narrative featuring human actions perceived or believed both by teller and listeners to have taken place within human history (of course, whether or not they actually happened is debatable). Examples include Paul Bunyan, Robin Hood, and La Llorona.  A variation is the tall tale, a story with unbelievable elements, related as if it were true and factual.  

Urban legends are a modern genre of folk tale that is rooted in local popular culture, usually comprising fictional stories that are often presented as true, with macabre or humorous elements. These legends can be used for entertainment purposes, as well as semi-serious explanations for seemingly-mysterious events, such as disappearances and strange objects.

A fairy tale, also called a wonder tale, magic tale, or Märchen (the German term), is a folklore genre that takes the form of a short story featuring entities such as dwarfs, dragons, elves, fairies, giants, gnomes, goblins, mermaids, talking animals, trolls, unicorns, or witches, and usually magic or enchantments. The oral tradition of the fairy tale came long before the written page. Tales were told or enacted dramatically, rather than written down, and handed down from generation to generation. While there are fairy tale elements in stories written as literature going back to the Renaissance and Baroque periods, fairy tales as we know them were first popularized by Wilhelm and Jacob Grimm in the 19th century. 

Image from Old French Fairy Tales by Comtesse De Segur; illustrated by Virginia Frances Sterrett; 1920

Myths are traditional, usually ancient, stories dealing with supernatural beings, ancestors, or heroes that serves as a fundamental type in the worldview of a people. The purpose of myths is to account for the origins of something, explain aspects of the natural world or delineate the psychology, customs, or ideals of society. In many myths, the main characters are gods or demi-gods and the story may have some religious meaning or background.

Statue of Mercury, Messenger of the Gods, Greece-Rome
Engraved by Claude Mellan, 1669, as part of the Tableaux du Cabinet du Roi of Louis XIV.