Are an elephant's "fingers" and human fingers the result of divergent evolution?
Yes, they are. Divergent evolution is the term for structures that have a similar anatomical origin, but which have accumulated mutations over time which have made them distinctively different in structure, in function, or in both.
In the case of fingers and toes, all mammals have descended from a common ancestor that apparently had a group of carpals, five metacarpals, and fifteen phalanges arranged in five rows. In some animals the bones have changed in length relative to one another; for instance, a bat's wing (which is actually its hand) has very long, very slender phalanges, while the phalanges of an elephant or a whale are very thick and stubby. Some animals, such as the horse, have lost a number of these bones entirely. So an elephant's foot bones and a human's hand and foot bones are a good example of divergent evolution.