To understand the differences between “cape” and “peninsula,” it helps to know the origins of the words. “Cape” comes from caput, the Latin word for “head.” It usually refers to a headland (note the connection to “head”) or a promontorya point of high land that juts into the sea. However, it can also be used for any point of land, high or low, that juts into the sea.
“Peninsula” comes from the Latin words paene, meaning “almost,” and insula, meaning “island.” So think of a peninsula as a piece of land that is almost an island. The term is usually used for a piece of land that is nearly surrounded by water and attached to a larger area of land by an isthmusa narrow strip of land. It can also refer to any piece of land that juts into the water, regardless of whether it has a well-defined isthmus.
A relatively small peninsula could also be a cape. However, “peninsula” is also used to describe much larger land areas. For example, the state of Florida (excluding the Panhandle area in the north) is considered a peninsula.
A peninsula can have capes along its edges. For example, Cabo (“Cape”) San Lucas sits at the southern tip of Mexico's Baja California peninsula, and other capes are found along the peninsula's east and west coasts.
The differences between “gulf” and “bay” are less straightforward. A gulf is defined as an area of an ocean or sea bordering on and lying within a curved coastline and usually larger than a bay and smaller than a sea. A bay is an inlet of the ocean or part of the ocean bordering on land and partly surrounded by land, or any small body of water set off from the main body of an ocean, lake, or gulf.
Comparing the definitions, you'll note that gulfs are usually larger than bays and can even have bays within them. For example, Tampa Bay and Galveston Bay are inlets of the Gulf of Mexico. You'll also note that gulfs are always part of an ocean or sea, whereas bays are also found in lakes.
If you study a detailed world map, you'll see that “bay” and “gulf” are used almost interchangeably. Although most gulfs are indeed larger than most bays, there are examples where the opposite is true. For example, the Bay of Bengal in southern Asia is much larger than gulfs such as the Gulf of Aden, the Gulf of Oman, and the Gulf of Tonkin.
(Question submitted by a teacher at Hastings Ninth Grade Center in Texas.)