hauberk vs chain mail

hauberk and chain mail both are nouns.

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

As nouns, chain mail is a hypernym of hauberk; that is, chain mail is a word with a broader meaning than hauberk:

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

Other hypernyms of hauberk include chain armor, chain armour, mail, ring armor, ring armour, ring mail.

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