there is a blur of definition and different use of names!
arguably, the largest sea in the world is the Pacific Ocean, but it is called an ocean!
The Caspian Sea is the largest enclosed sea, perceived as a sea by its ancient inhabitants because of some salinity ! - BUT it is 'technically' a lake. (The Caspian Sea is a remnant of the Tethys Ocean, which also included the Black Sea and the Mediterranean - it became landlocked due to continental drift)
The largest sea (that is part of an ocean) by area is The South China Sea - the next largest are The Caribbean Sea, followed by the Mediterranean)
Areas are argued over because boundaries are not agreed!
(And another name for a sea ... Gulf of Mexico!)