jenny wren vs wren

jenny wren and wren both are nouns.

Word	Noun	Adjective	Verb	Adverb
jenny wren	Yes	No	No	No
wren	Yes	No	No	No

As nouns, jenny wren and wren are synonyms defined as:

jenny wren and wren: any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects

jenny wren (noun)	wren (noun)
any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects	any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects