certiorari vs writ

certiorari and writ both are nouns.

Word	Noun	Adjective	Verb	Adverb
certiorari	Yes	No	No	No
writ	Yes	No	No	No

As nouns, writ is a hypernym of certiorari; that is, writ is a word with a broader meaning than certiorari:

certiorari: a common law writ issued by a superior court to one of inferior jurisdiction demanding the record of a particular case
writ: (law) a legal document issued by a court or judicial officer

Other hypernyms of certiorari include judicial writ.

certiorari (noun)	writ (noun)
a common law writ issued by a superior court to one of inferior jurisdiction demanding the record of a particular case	(law) a legal document issued by a court or judicial officer