rarity vs peculiarity

rarity and peculiarity both are nouns.

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

As nouns, rarity and peculiarity are synonyms defined as:

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

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

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