rare vs rarefied

rare and rarefied both are adjectives.

Word	Noun	Adjective	Verb	Adverb
rare	No	Yes	No	No
rarefied	No	Yes	No	No

As adjectives, rare and rarefied are synonyms defined as:

Other synonyms of rare include rarified.

rare (adjective)	rarefied (adjective)
marked by an uncommon quality; especially superlative or extreme of its kind	of high moral or intellectual value; elevated in nature or style
recurring only at long intervals	having low density
(of meat) cooked a short time; still red inside
not widely distributed
having low density
not widely known; especially valued for its uncommonness