common canary vs canary bird

common canary and canary bird both are nouns.

Word	Noun	Adjective	Verb	Adverb
common canary	Yes	No	No	No
canary bird	Yes	No	No	No

As nouns, canary bird is a hypernym of common canary; that is, canary bird is a word with a broader meaning than common canary:

common canary: native to the Canary Islands and Azores; popular usually yellow cage bird noted for its song
canary bird: any of several small Old World finches

Other hypernyms of common canary include canary.

common canary (noun)	canary bird (noun)
native to the Canary Islands and Azores; popular usually yellow cage bird noted for its song	any of several small Old World finches