distinguishing characteristic vs peculiarity

distinguishing characteristic and peculiarity both are nouns.

Word	Noun	Adjective	Verb	Adverb
distinguishing characteristic	Yes	No	No	No
peculiarity	Yes	No	No	No

As nouns, distinguishing characteristic and peculiarity are synonyms defined as:

distinguishing characteristic and peculiarity: an odd or unusual characteristic

Other synonyms of distinguishing characteristic include distinctive feature.

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