pole star vs Polaris

pole star and Polaris both are nouns.

Word	Noun	Adjective	Verb	Adverb
pole star	Yes	No	No	No
Polaris	Yes	No	No	No

As nouns, pole star and Polaris are synonyms defined as:

pole star and Polaris: the brightest star in Ursa Minor; at the end of the handle of the Little Dipper; the northern axis of the earth points toward it

Other synonyms of pole star include North Star, polar star, polestar.

pole star (noun)	Polaris (noun)
the brightest star in Ursa Minor; at the end of the handle of the Little Dipper; the northern axis of the earth points toward it	the brightest star in Ursa Minor; at the end of the handle of the Little Dipper; the northern axis of the earth points toward it