bra vs brassiere

bra and brassiere both are nouns.

Word	Noun	Adjective	Verb	Adverb
bra	Yes	No	No	No
brassiere	Yes	No	No	No

As nouns, bra and brassiere are synonyms defined as:

bra and brassiere: an undergarment worn by women to support their breasts

Other synonyms of bra include bandeau.

bra (noun)	brassiere (noun)
an undergarment worn by women to support their breasts	an undergarment worn by women to support their breasts