Carolina parakeet vs parrakeet

Carolina parakeet and parrakeet both are nouns.

Word	Noun	Adjective	Verb	Adverb
Carolina parakeet	Yes	No	No	No
parrakeet	Yes	No	No	No

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

Carolina parakeet: extinct parakeet whose range extended far into the United States
parrakeet: any of numerous small slender long-tailed parrots

Other hypernyms of Carolina parakeet include parakeet, paraquet, paroquet, parroket, parroquet.

Carolina parakeet (noun)	parrakeet (noun)
extinct parakeet whose range extended far into the United States	any of numerous small slender long-tailed parrots