Coral Sea vs battle of the Coral Sea

Coral Sea and battle of the Coral Sea both are nouns.

Word	Noun	Adjective	Verb	Adverb
Coral Sea	Yes	No	No	No
battle of the Coral Sea	Yes	No	No	No

As nouns, Coral Sea and battle of the Coral Sea are synonyms defined as:

Coral Sea and battle of the Coral Sea: a Japanese defeat in World War II (May 1942); the first naval battle fought entirely by planes based on aircraft carriers

Coral Sea (noun)	battle of the Coral Sea (noun)
a Japanese defeat in World War II (May 1942); the first naval battle fought entirely by planes based on aircraft carriers	a Japanese defeat in World War II (May 1942); the first naval battle fought entirely by planes based on aircraft carriers
an arm of the South Pacific to the northeast of Australia