Newton's law vs law of motion

Newton's law and law of motion both are nouns.

Word	Noun	Adjective	Verb	Adverb
Newton's law	Yes	No	No	No
law of motion	Yes	No	No	No

As nouns, Newton's law and law of motion are synonyms defined as:

Newton's law and law of motion: one of three basic laws of classical mechanics

Other synonyms of Newton's law include Newton's law of motion.

Newton's law (noun)	law of motion (noun)
one of three basic laws of classical mechanics	one of three basic laws of classical mechanics