Both techniques define the art of playing a guitar by plucking the strings exclusively with the fingers.
From this perspective we can consider the classical guitar as the first example of fingerpicking in the history of the guitar.
Looking at the matter from a deeper technical perspective, classical guitar technique and fingerstyle technique can be extremely different; not only because the former is used exclusively on a nylon string guitar while the latter on nylon and metal strings, but above all because the classical guitar goes back centuries, with different schools and teachers.
Fingerpicking, on the other hand, is relatively new and not as precise and well defined as the classical style.