As I understand, the distinction between "Folklore" (originating as an oral tradition) and "Fakelore" (the intentional creation of an oral tradition) is an issue of "authenticity" as measured in the antiquity of the particular story.
For example, in my part of the world I hear the term "fakelore" most often in regards to Pecos Bill which is sometimes claimed to be a literary invention of the early 20th century that was passed off as a story with greater antiquity (i.e. the 19th century) than it really has. How much is that true for Pecos Bill specifically, but more importantly, is that an important distinction in the study of folklore or does the distinction place too much emphasis on "authenticity" (however that is constructed).
American folklorist Richard Dorson (1916-1981) invented the term "fakelore" in 1950 to describe just the sort of thing represented by Pecos Bill - namely the literary invention of something that seems like oral tradition, which was then passed off as real folklore, but which never had roots in anything that was transmitted orally by the "folk."
Although it was once very much in vogue, the term has fallen out of favor with folklorists for several reasons. The first fundamental problem is that it does not given proper credit to the very real circumstance involving a steady flow between oral tradition and literature. For as long as people have written things down oral tradition has affected what was written and what was written has affected oral tradition.
The term fakelore implies that "really good folklore" is something that has emerged purely from the oral tradition without being tainted by what was written. But if that is the definition for the ideal expression of folklore, then one is not likely to find that Holy Grail. Even if the effect of literature on an aspect of oral tradition in a literate society is not apparent, at some point it likely existed.
In addition, the term fakelore implies that one aspect of culture (a "pure" expression of folklore) is superior to another (a literary story crafted to seem like oral tradition). We should not be in the business of judging elements of culture in this or in any other way.
The fact is, every source requires source criticism. Any historian just like any folklorists whose been around the block sufficiently has been "taken in" by a source at one point of another. We have assumed the source to have a level of integrity or a sort of context that is not borne out over time. The story of Pecos Bill is not fake or of limited value. It is an interesting literary attempt to create what might seem to be an oral tradition for a region. There is no problem with the story as long as one is not "taken in," as long as one does not see in something a thing that is not there.
The Donation of Pepin is a fascinating document that reveals a great deal. Source criticism puts it in perspective and the astute historian knows not to take it on face value. But the document has value. Similarly, the astute folklorist must attempt to apply similar source criticism for sources available for study. An old friend of mine, the late Warren d’Azevedo (1920-2014) once told me that when he was doing ethnographic work with the Washoe Indians showed him something they called the Eagle Dance, a performance that involved wings and the appearance of the eagle wheeling around. It was a beautiful tradition, and Warren was really impressed because neighboring tribes did not seem to have it. He was asking the elders about it, and they said that a movie director had taught it to them for a film he was making. They liked it and so they kept it. On one level this could be regarded as fakelore, but in fact is was a very nice tradition that just happened not to have very deep roots. With the right perspective, an aspect of culture is merely an aspect of culture. It is neither good nor bad. The only thing that can be bad is not fully understanding its context.
edited to add date of Dorson's work.