I tried to address this in the article I did on "Fingerstyle" in Acoustic Guitar a few months ago. As with anything, you sort of have to ask the person saying it what they mean, since it's not like there's some authoritative definition.
But, what I tried to make the case for was that fingerstyle is a larger encompassing term. Tho some use it to mean a "style", it makes more sense as a technique. Andy McKee plays fingerstyle, but so does Joe Pass, Segovia, and Paco de Lucia. Jeff Beck, as well. Fingerpicking is more commonly understood to refer to a folk/roots sort of approach, anyone from Elizabeth Cotten to Chet Atkins and Merle Travis. Travis picking, etc.
But a rose by any other name.... You can check out my attempt to thread the needle and demonstrate some of the range of options here:
https://acousticguitar.com/learn-fin...ar-essentials/