pope's nose vs parson's nose

pope's nose and parson's nose both are nouns.

Word	Noun	Adjective	Verb	Adverb
pope's nose	Yes	No	No	No
parson's nose	Yes	No	No	No

As nouns, pope's nose and parson's nose are synonyms defined as:

pope's nose (noun)	parson's nose (noun)
the tail of a dressed fowl	the tail of a dressed fowl