Bahama Islands vs Commonwealth of the Bahamas

Bahama Islands and Commonwealth of the Bahamas both are nouns.

Word	Noun	Adjective	Verb	Adverb
Bahama Islands	Yes	No	No	No
Commonwealth of the Bahamas	Yes	No	No	No

As nouns, Bahama Islands and Commonwealth of the Bahamas are synonyms defined as:

Bahama Islands and Commonwealth of the Bahamas: island country in the Atlantic to the east of Florida and Cuba; a popular winter resort

Other synonyms of Bahama Islands include Bahamas.

Bahama Islands (noun)	Commonwealth of the Bahamas (noun)
island country in the Atlantic to the east of Florida and Cuba; a popular winter resort	island country in the Atlantic to the east of Florida and Cuba; a popular winter resort