* Amherst College: A highly selective, private liberal arts college. This is generally what people mean when they say "Amherst."
* University of Massachusetts Amherst (UMass Amherst): A large, public research university. Often referred to as just UMass Amherst.
There are also smaller institutions and programs in Amherst, but Amherst College and UMass Amherst are by far the largest and most well-known.