peculiarity vs rarity

peculiarity and rarity both are nouns.

Word	Noun	Adjective	Verb	Adverb
peculiarity	Yes	No	No	No
rarity	Yes	No	No	No

As nouns, peculiarity and rarity are synonyms defined as:

peculiarity and rarity: something unusual -- perhaps worthy of collecting

Other synonyms of peculiarity include curio, curiosity, oddity, oddment.

peculiarity (noun)	rarity (noun)
something unusual -- perhaps worthy of collecting	something unusual -- perhaps worthy of collecting
a distinguishing trait	a rarified quality
an odd or unusual characteristic	noteworthy scarcity