The only sea on Earth that is defined by ocean currents rather than a land border is the Sargasso Sea.
The Sargasso Sea is a vast patch of ocean named for a genus of free-floating seaweed called Sargassum. While there are many different types of algae found floating in the ocean all around the world, the Sargasso Sea is unique in that it harbors species of sargassum that are 'holopelagi' - this means that the algae not only freely float around the ocean, but it reproduces vegetatively on the high seas. Other seaweeds reproduce and begin life on the floor of the ocean.
Sargassum provides a home to an amazing variety of marine species. Turtles use sargassum mats as nurseries where hatchlings have food and shelter. Sargassum also provides essential habitat for shrimp, crab, fish, and other marine species that have adapted specifically to this floating algae. The Sargasso Sea is a spawning site for threatened and endangered eels, as well as the white marlin, porbeagle shark, and dolphinfish. Humpback whales annually migrate through the Sargasso Sea. Commercial fish, such as tuna, and birds also migrate through the Sargasso Sea and depend on it for food.
While all other seas in the world are defined at least in part by land boundaries, the Sargasso Sea is defined only by ocean currents. It lies within the Northern Atlantic Subtropical Gyre. The Gulf Stream establishes the Sargasso Sea's western boundary, while the Sea is further defined to the north by the North Atlantic Current, to the east by the Canary Current, and to the south by the North Atlantic Equatorial Current. Since this area is defined by boundary currents, its borders are dynamic, correlating roughly with the Azores High-Pressure Center for any particular season.