"I only really like Jazz when it's folk music, which is where it started."

All types of music have their origins in folk and can be traced back to folk tunes and songs of some description.

By that token you could say "I only like classical when its folk - which is where it started" and not be incorrect.

yet by the very definitions used in both of the above sentences we see a distinction between two types of music, identified by the terms used to describe them.

In your sentence, the terms "jazz" and "folk", in my sentence the terms "jazz" and "folk".

So how do we decide which term to use?

we have to establish some kind of boundary or borderline between the two genres.

How do we do that?

By identifying what is unique about each.

Jazz is distinct from folk in its use of muliple key centres.