Actually, these are different genres of music, often interpreted with different guitars.
CLASSICAL MUSIC REPERTOIRE PLAYED WITH THE FINGERS ON CLASSICAL GUITAR WITH NYLON STRINGS
REPERTOIRE OF BLUES MUSIC PLAYED WITH THE FINGERS ON ACOUSTIC GUITAR WITH METAL STRINGS
REPERTOIRE OF JAZZ MUSIC PLAYED WITH THE FINGERS OFTEN ON AN ARC-TOP
SEMIACOUSTIC GUITAR WITH METAL STRINGS
In more technical-musical terms, fingerstyle, in addition to what has been said, can also refer to an execution of guitar played in counterpoint.
We can produce the counterpoint by performing two different lines at the same time: the melody line with trebles and the accompaniment line with basses. This allows the guitarist more complete and self-sufficient performances. Both lines play independently.
The term ‘fingerpicking’ instead, regards the technique originated on the acoustic guitar with American music, mainly the blues and the country.
More precisely, it refers to “primitive fingerstyle techniques” introduced by the pioneers of blues and American folk. Therefore this term is linked to a specific musical genre.
To further clarify, we can say that a bluesman, pioneer of the blues, played fingerpicking, but a guitarist of our days playing blues, plays fingerstyle blues.