vestment vs pallium

vestment and pallium both are nouns.

Word	Noun	Adjective	Verb	Adverb
vestment	Yes	No	No	No
pallium	Yes	No	No	No

As nouns, pallium is a hyponym of vestment; that is, pallium is a word with a more specific, narrower meaning than vestment:

vestment: gown (especially ceremonial garments) worn by the clergy
pallium: (Roman Catholic Church) vestment consisting of a band encircling the shoulders with two lappets hanging in front and back

Other hyponyms of vestment include alb, cassock, chasuble, humeral veil, veil, pontifical, surplice.

vestment (noun)	pallium (noun)
gown (especially ceremonial garments) worn by the clergy	cloak or mantle worn by men in ancient Rome
	(Roman Catholic Church) vestment consisting of a band encircling the shoulders with two lappets hanging in front and back
	(zoology) a protective layer of epidermis in mollusks or brachiopods that secretes a substance forming the shell
	the layer of unmyelinated neurons (the grey matter) forming the cortex of the cerebrum