The Caribbean is a subregion of the Americas that includes the Caribbean Sea and its islands, some of which are surrounded by the Caribbean Sea and some of which border both the Caribbean Sea and the North Atlantic Ocean; the nearby coastal areas on the mainland are sometimes also included in the region. The region is south-east of the Gulf of Mexico and Northern America, east of Central America, and north of South America.
The Battle of the Saintes between British and French fleets in 1782, by Nicholas Pocock
The West Indies is a subregion of North America, surrounded by the North Atlantic Ocean and the Caribbean Sea, which comprises 13 independent island countries and 19 dependencies in three archipelagos: the Greater Antilles, the Lesser Antilles, and the Lucayan Archipelago.
The subduction of the South American Plate and part of the North American Plate beneath the Caribbean Plate produces both the Puerto Rico Trench, the deepest part of the Atlantic Ocean, as well as the active volcanoes of the Lesser Antilles (bottom left of the image, south of the Virgin Islands)