diplomatic pouch vs mail pouch

diplomatic pouch and mail pouch both are nouns.

Word	Noun	Adjective	Verb	Adverb
diplomatic pouch	Yes	No	No	No
mail pouch	Yes	No	No	No

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

diplomatic pouch: a mail pouch that is sealed shut and that is used to carry communications between a legation and its home office
mail pouch: pouch used in the shipment of mail

Other hypernyms of diplomatic pouch include mailbag.

diplomatic pouch (noun)	mail pouch (noun)
a mail pouch that is sealed shut and that is used to carry communications between a legation and its home office	pouch used in the shipment of mail