pole star vs polar star

pole star and polar star both are nouns.

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

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

pole star and polar star: 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, Polaris, polestar.

pole star (noun)	polar star (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