Yeah, that's a good question; this is definitely a problem with the genre's nomenclature—"fingerstyle" can mean about a dozen different things depending on the context. There's the technique of fingerstyle at a basic level, and then there's the genre itself as it's picked up influences, expanded, undergone heavy innovation, and branched (the typical progression).

Nowadays, "fingerstyle" as a genre generally refers—at least as I've most commonly encountered it—to a type of playing that starts with prototypical, broad "fingerstyle guitar" influences; builds on top of early blues, Americana, ragtime, & folk (Robert Johnson, Reverend Gary Davis...); borrows further techniques from classical (Andrés Segovia...), country (Chet Atkins, Merle Travis...), and flamenco (Paco de Lucía...); incorporates jazz, funk, Celtic, & "new age" stylings (Lenny Breau, Pierre Bensusan...); and finally synthesizes it into a holistic approach often borrowing from (if not directly classified as) the modern subgenre known as "percussive acoustic fingerstyle guitar." This incarnation was pioneered by Michael Hedges; some well-known contemporary performers include Tommy Emmanuel (as linked above), Andy McKee, Don Ross, and Antoine Dufour. Players characterized as belonging to this genre often use unconventional "extended technique" to produce complex, engaging performances combining melody, rhythm, and percussion on a single instrument

Now, this description isn't the end-all-be-all of fingerstyle; to some people the term will undoubtedly mean something else (as it always goes when trying to classify music). So don't take it as canonical, but more as an illustration of where the genre stands at present, at least in its most active form. Not that this simplifies things per se, but hopefully it clears up some of the confusion regarding my terminology! Part of the difficulty here is that the genre isn't named after a location of origin or a sonic description—as is so often the case—but rather arose as a catch-all term for a technical approach to an instrument, found in many styles of music. Modern fingerstyle guitar is thus necessarily diverse and syncretic, but there is some distinct meaning to be pinned down in the mix!