The term was coined in 1846 by an Englishman who wanted to use an Anglo-Saxon term for what was then called "popular antiquities". Johann Gottfried von Herder first advocated the deliberate recording and preservation of folklore to document the authentic spirit, tradition, and identity of the German people; the belief that there can be such authenticity is one of the tenets of the romantic nationalism which Herder developed.
While folklore can contain religious or mythic elements, it typically concerns itself with the mundane traditions of everyday life. Folklore frequently ties the practical and the esoteric into one narrative package. It has often been conflated with mythology, and vice versa, because it has been assumed that any figurative story that does not pertain to the dominant beliefs of the time is not of the same status as those dominant beliefs. Thus, Roman religion is called "myth" by Christians. In that way, both myth and folklore have become catch-all terms for all figurative narratives which do not correspond with the dominant belief structure.
Sometimes "folklore" is religious in nature, like the tales of the Welsh Mabinogion or those found in Icelandic skaldic poetry. In this case, folklore is being used in a quasi-pejorative sense. That is, while the tales of Odin the Wanderer have a religious value to the Norse who wrote the stories, because it does not fit into a Christian configuration it is not "religious" per se. Instead it is "folklore."
On the other hand, folklore can be used to accurately describe a figurative narrative which has no theological or religious content, but instead pertains to useful mundane lore. This mundane lore may or may not have components of the fantastic[?] (such as magic, ethereal beings or the absurdist personification of inanimate objects). These folktales may emerge from a religious tradition, but are essentially secular. "Hansel and Grethel" is a strong example of this fine line. While the element of witchcraft may possibly contain a religious subtext, or at least imply some early euro-pagan origin (like what Margaret Murray or The Golden Bough might describe), it can be said with some degree of certainty that the purpose of the tale is primarily one of mundane instruction regarding forest safety, as well as secondarily a cautionary tale about the dangers of famine to large families. There is moral scope to the work, but not necessarily a religious scope.
The modern western folklore that we are faced has been identified by some scholars as that of urban legend and conspiracy theory. Only time will tell what of that tradition is practical, what is ephemeral and what is religious. "Hansel and Gretel[?]" lives on today in the tales that inspired the Texas Chainsaw Massacre film. But UFO abduction narratives can be seen, in some sense, to refigure the tales of pre-Christian Europe... or even such tales in the Bible as the Ascent of Elijiah to Heaven in a spinning wheel. Are these "folktales"? Or is their religious dimension being purposefully, if unconsciously, ignored or suppressed?