The following summary of definitions of folktale and fairytale from my draft Introduction to Folklore (to be e-published in September), may be of use; feel free to ask questions:

Folktales – or Märchen, using the German, technical term – are longer stories with more than one episode. They are restricted, in theory at least, to evening presentation. A folktale is not to be believed, taking place in a fantastic setting. The European folktale also requires a happy ending, the cliché of “happily ever after.” Any given folktale can be told with considerable variation, but they are traditional in basic form, and folklorists have spent decades tracing the history and distribution of these stories.

A word here about the term “fairytale” is appropriate. At the end of the eighteenth century, various writers, most prominently the Grimm brothers, began publishing children’s stories based on folktales. These collections became extremely popular, particularly among the urban and increasingly literate emerging middle class as it found itself removed from the peasant soil that served as home to the stories. Fairytales often cause misunderstandings. In a culture that knows more about fairytales than Märchen, people assume that the folktale was intended for children. This is certainly not the case since the stories were often violent or sexual in ways thought inappropriate for children. Indeed, the telling of a folktale was usually delayed until the children had gone to bed. While fairytales provide the modern reader with the easiest access to the many stories that were once told internationally, one should always realize that they are removed from the primary inspiration. The original stories and their content provided serious entertainment for adults and they were part of an oral tradition, not something that was fossilized in writing.

The evolution of fairytales had a profound effect on the subject of fairies, elves, trolls, and similar entities. Because fairytales became the literary domain of children, many people – including writers and publishers – assumed the same was true of the supernatural beings. In their original context, nothing could be further from the truth. These were not cute, diminutive creatures whose sole purpose was to delight children. They were powerful, dangerous, and capable of great harm. The European peasantry feared and respected them, and their stories underscore this, conveying in uncompromising terms the code of ethics and behavior that one must employ to survive an encounter with the dangerous world of magic and power.

The resident folklorist has done a great job answering the question, but I have a bit more to add to the pot. The original source of these stories is really unknown, as they were much older oral tales that were put to paper only centuries after they had been passed around from culture to culture and between social groups. Many original tale variations, like Bluebeard, Beauty and the Beast, and Vasalisa the Beautiful, were thought to have been told by women to pubescent girls during household work or spinning sessions (thus the term "spinning a yarn" or "weaving a tale". Lots of the tales outline common fears that these girls would face in their impending adulthood. Marriage to a complete stranger was a common occurrence and many girls feared the marriage bed, and "beastly" advances of men they didn't know. Some of these tales were cautionary and some were uplifting in their theme of love changing a man from a beast into a prince. Tales like Vasalisa and similar tale types outline duties expected of a woman. You might be familiar with the tales where a girl meets an older woman and has to perform a series of tasks. These tasks are often related to spinning, hard-work, upright moral conduct, etc. and the girl is usually rewarded when she completes these tasks and proves herself to be fit for the transition to the adult stage of life.

Other tales, such as Hansel and Gretel or Little Red Riding Hood were reflections of very real issues that the common people faced. Starvation and highway robbers lurking in the woods were every day dangers that figured highly in these tales and were often softened a bit once the Brothers Grimm adapted their original collection for children's readership.

Original tales have, over the years, been adapted to suit cultural changes and trends. Many tales were introduced to the French court and given trappings of bourgeoisie that were not included in the original tales at all, but were appealing to the salons where nobles gathered and enjoyed them. Even the texts written down by the Grimms were not actually sourced from peasant women, as some may claim, but from women who were of French origin and also included tales by Perrault.

If you'd like a good book that I find is a great starter for how to analyze fairy tales, check out Little Red Riding Hood Uncloaked by Catherine Orenstein. It features a lot of good information on the background tale, variations, and how it has been included in modern popular culture and advertising. That book launched my interest in folklore and once read, it makes it obvious at how fairy tales continue to evolve and permeate so many aspects of our lives.