Carolina wren vs jenny wren

Carolina wren and jenny wren both are nouns.

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

As nouns, jenny wren is a hypernym of Carolina wren; that is, jenny wren is a word with a broader meaning than Carolina wren:

Carolina wren: large United States wren with a musical call
jenny wren: any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects

Other hypernyms of Carolina wren include wren.

Carolina wren (noun)	jenny wren (noun)
large United States wren with a musical call	any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects