Over at Mania.com, Niko Silvester presents a concise and well-written essay on the use of mythology, often associated with religion, and folklore in anime. The brunt of it focuses on context, including the definitions of these terms, which I find very interesting.
I want to add that the connotation of folklore is often old and ancient – I think people standing around a campfire telling stories in days gone by. But in reality, folklore can be very current. For instance, if your dad told you the story of your great-uncle saving three kids from drowning, but there is no newspaper article or other account to support this tale – you have folklore. It’s the unsupported side of history.
Silvester then discusses probably the most known intersection of folklore and mythology with anime and manga in Journey to the West. Take a read!