"Fingerstyle" encompasses all types of playing with your fingers. It's also more of a classical term, wheras if you were playing a folk tune with your fingers you would most likely hear it referred to as "fingerpicking." Travis picking refers to a certain style where the thumb plays an alternating bassline and the index and middle fingers play alternating treble notes. Here's a Wikpedia article on the whole subject:

http://en.wikipedia.org/wiki/Travis_picking#Travis_picking