Bess Lomax Hawes put it aptly in her lovely autobiography, "Sing It Pretty".

The folk process is "stability and change" or "stability and adaptability".

A song has roots in a tradition but it gets changed a little by a new environment or need.

Sometimes the changes are imperceptible. Usually the theme/story of the song is constant but changes in the way it's told.

Parodies can sometimes be picked up as part of this process. "Yankee Doodle" for example or "Dixie".

Colorful lines are adapted to speech patterns from certain cultural groups or people from geographical areas such as the country of the US South.

"I will twine midst the ringlets of raven black hair" becomes:
"I will twine and will mingle my raven black hair"......(mondigreens, sometimes)

All you have to do is research texts that have taken place over the years to see the changes. "Evolution" is a perfect metaphor for the folk song. There are branches that go back to antiquity stemming from different lines.

Sometimes there can be a conscious re-write of a lyric.

Often what you see in folk song books are "collated" texts coming from different song "variants". The Lomaxes did this in their books.

I like collated texts if they tell the story in a concise and interesting manner.

Usually, just like basket making, any deviation from the process is not radical.
Basketry has been done the same way for centuries but there are variations.
Quilt making might be another analogy.

Here's a conundrum, though. Folklorists and folk musicologists have changed their definitions over time. For example, Cecil Sharp considered the American five-string banjo a bowdlerization of the Anglo-American ballad in the way that a folk song played on an electric guitar with a drum set might not set well with "purists". In this way, I think of African-American blues as a folk music but some might not.

Still blues is "stability and change".

I think that the essential difference stems from a familiarity with the style of playing or singing and the song material. Also, does the person who learned the song qualify as an "informant" or carrier of that song having learned it from their childhood? I learned a blues holler from my step-father that I have not heard anywhere else. There are variants of it but not the same way as I know it. I think this qualifies it as a folk song. No one knows the original composer or author of it.

I hope this sheds some light on this "process" or "processes" if you like.