mail vs coat of mail

mail and coat of mail both are nouns.

Word	Noun	Adjective	Verb	Adverb
mail	Yes	No	Yes	No
coat of mail	Yes	No	No	No

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

Other hypernyms of mail include body armor, body armour, cataphract, suit of armor, suit of armour.

mail (noun)	coat of mail (noun)
(Middle Ages) flexible armor made of interlinked metal rings	armor that protects the wearer's whole body
a conveyance that transports the letters and packages that are conveyed by the postal system
the system whereby messages are transmitted via the post office
the bags of letters and packages that are transported by the postal service
any particular collection of letters or packages that is delivered

mail (verb)	coat of mail (verb)
cause to be directed or transmitted to another place
send via the postal service