"Stainless Steel Case" is used to refer to the whole watch being stainless steel. Plated base metal usually has a more nickel-like, more white or silver finish than steel. Also the links in a base metal band will often have a mold line, a raised line of metal, usually on an inside portion of the link. The plating kind of gives the seam a bit of a covered over look.
The reason base metal is used is because it is cheap. Base metal is any combination of metals other than precious(copper, brass, tin, lead, and nickel to name a few). After the plating wears off the metal underneath tends get very pitted. Both the plating and the base metal can cause allergic reactions. Stainless steel is hypo-allergenic for almost everyone. It is also harder, more expensive to work with and far more durable.
Case materials can be a significant portion of the cost of producing the watch. There are different grades of stainless steel and different ways of forming it. Inexpensive steel watches will often use folded links in the watchband. They are folded from sheet metal and are identifiable by open seams and light weight. Better links are either cast or machined and are solid and heavier.
