This is one of those confusing terms, where the word for a technique has come to mean a musical style. We have much the same situation with "flatpicking" where if you take it literally, then anyone who plays with a flat pick (rock players, jazz players, etc) would be flatpicking. But instead it usually means a specific style of music, that you sort of know when you hear it. "Fingerstyle" usually means playing on a steel string guitar, and there's a tendency to use or at least accept alternate tunings (by no means universal), and to play one's own compositions (again, not at all universal). Fingerstyle is often thought of as being influenced by folk music, pop music, and often gets labeled "new age" because of some of the Windham Hill pioneers in "fingerstyle". To make it more confusing, there are "fingerpickers" who vehemently resist the name "fingerstyle", even tho they share a lot in common, tho "fingerpickers" usually fall more into the Chet Atkins camp, or country blues, or... And of course, you have "fingerstyle" players like Muriel Anderson, who mostly plays a classical guitar, and steel string players like Peppino d'Agostino, and Peter Finger who sometimes play classical on a steel string. Or Michael Chapdelaine, a classical guitar professor, who most often plays on a steel string, and might play Bach one minute and Hang On Sloopy the next.
The main thing is, as Rick said, the techniques are very similar, with the classical approach tending to be a little more organized and methodical, so learn from both, and play what you like!
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