habeas corpus vs writ of habeas corpus

habeas corpus and writ of habeas corpus both are nouns.

Word	Noun	Adjective	Verb	Adverb
habeas corpus	Yes	No	No	No
writ of habeas corpus	Yes	No	No	No

As nouns, habeas corpus and writ of habeas corpus are synonyms defined as:

habeas corpus and writ of habeas corpus: a writ ordering a prisoner to be brought before a judge

habeas corpus (noun)	writ of habeas corpus (noun)
the civil right to obtain a writ of habeas corpus as protection against illegal imprisonment	a writ ordering a prisoner to be brought before a judge
a writ ordering a prisoner to be brought before a judge