Shearling is a kind of fur that comes from sheep or lamb. The wool is attatched one side while the other side is suede. Shearling has a very soft texture when compared to sherpa since it is from the real animal. It is most recognizeable in classic aviator jackets or warm winter coats. Additionally it can be seen in boots and shoes like Uggs.
Sherpa is a type of fleece made of either cotton, polyester, or a blend of both. Sherpa is often called faux-sheepskin or faux-shearling, simply because it is made to mimic shearling. It is much more affordable than shearling but serves the same purposes.
Overall, sherpa is the more common material since it can be synthetic. It is not harvested from animals, while shearling is. They are both very warm materials, great for winter time.
Check out this article on fleeces and similar pieces from different brands!