peculiarity vs distinctiveness

peculiarity and distinctiveness both are nouns.

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

As nouns, peculiarity and distinctiveness are synonyms defined as:

Other synonyms of peculiarity include speciality, specialness, specialty.

peculiarity (noun)	distinctiveness (noun)
something unusual -- perhaps worthy of collecting	utter dissimilarity
a distinguishing trait	a distinguishing trait
an odd or unusual characteristic