idiosyncrasy vs peculiarity

idiosyncrasy and peculiarity both are nouns.

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

As nouns, peculiarity is a hypernym of idiosyncrasy; that is, peculiarity is a word with a broader meaning than idiosyncrasy:

idiosyncrasy: a behavioral attribute that is distinctive and peculiar to an individual
peculiarity: a distinguishing trait

Other hypernyms of idiosyncrasy include distinctiveness, speciality, specialness, specialty.

idiosyncrasy (noun)	peculiarity (noun)
a behavioral attribute that is distinctive and peculiar to an individual	something unusual -- perhaps worthy of collecting
	a distinguishing trait
	an odd or unusual characteristic