polar star vs pole star

polar star and pole star both are nouns.

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

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

polar star and pole 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 polar star include North Star, Polaris, polestar.

polar star (noun)	pole 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