cactus wren vs jenny wren

cactus wren and jenny wren both are nouns.

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

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

cactus wren: large harsh-voiced American wren of arid regions of the United States southwest and Mexico
jenny wren: any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects

Other hypernyms of cactus wren include wren.

cactus wren (noun)	jenny wren (noun)
large harsh-voiced American wren of arid regions of the United States southwest and Mexico	any of several small active brown birds of the Northern Hemisphere with short upright tails; they feed on insects