What is the difference between a self rimming drop in sink and a undermount sink? Is the installation about the same?

With a self-rimming sink or drop in, the countertop fabricators will cut the appropriate hole and it drops in. The rim supports the sink on the top of the countertop. This is the easiest method of installing a sink, an added feature is the the built-in sink rim hides any minor flaws in the hole.

With an undermount sink, the countertop must be cut to the exact specification and have an added finish to the edges since it will be exposed.  The sink is held in place with brackets that attach to the underside of the counter.