chain mail vs hauberk

chain mail and hauberk both are nouns.

Word	Noun	Adjective	Verb	Adverb
chain mail	Yes	No	No	No
hauberk	Yes	No	No	No

As nouns, hauberk is a hyponym of chain mail; that is, hauberk is a word with a more specific, narrower meaning than chain mail:

chain mail: (Middle Ages) flexible armor made of interlinked metal rings
hauberk: a long (usually sleeveless) tunic of chain mail formerly worn as defensive armor

Other hyponyms of chain mail include brigandine, habergeon, byrnie, gusset, voider.

chain mail (noun)	hauberk (noun)
(Middle Ages) flexible armor made of interlinked metal rings	a long (usually sleeveless) tunic of chain mail formerly worn as defensive armor