law of nations vs international law

law of nations and international law both are nouns.

Word	Noun	Adjective	Verb	Adverb
law of nations	Yes	No	No	No
international law	Yes	No	No	No

As nouns, law of nations and international law are synonyms defined as:

law of nations and international law: the body of laws governing relations between nations

law of nations (noun)	international law (noun)
the body of laws governing relations between nations	the body of laws governing relations between nations