peculiarity vs distinguishing characteristic

peculiarity and distinguishing characteristic both are nouns.

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

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

peculiarity and distinguishing characteristic: an odd or unusual characteristic

Other synonyms of peculiarity include distinctive feature.

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