There are two types of scallops commonly used in cooking: sea scallops and the smaller bay scallops.

Sea scallops are by far the most common. They are larger, somewhat tougher (although by no means tough unless badly overcooked), and much less expensive. Sea scallops can be an inch to two inches in diameter; they can be skewered and grilled, wrapped in bacon, and prepared in otherways that expose them to fierce heat. Sea scallops are available year-round.

If a recipe calling for scallops does not specify which type of scallops to use, it almost always refers to sea scallops.

Bay scallops are much smaller, sweeter, more tender, and two to three times as expensive as sea scallops. The season is short, just the winter and often over by mid-January or even by New Year's Day.

Because bay scallops are so small, they cook quickly. I like them sauteed quickly in butter or bacon fat. When I use butter, I usually deglaze the pan with a splach of dry vermouth, which I reduce for a moment and use as a sauce under the scallops. 

Bay scallops are now being farmed in China and Florida. If the fishmarket calls them Cape Cod or Nantucket scallops, then they are saying they are local bay scallops. This is a Good Thing, because the others get harvested, packaged, and shipped from far-off lands, so they are clearly not as fresh and may have been adulterated along the way - if you see Bay scallops in the supermarket for $3.99/lb, those are old frozen Chinese bay scallops that will not have the sweet nutty delicious character of the local Cape Cod scallops. Fresh local bay scallops in season are more likely to cost $25.99/lb, but as in so many foodie endeavors, you get what you pay for!