family Paridae vs bird family

family Paridae and bird family both are nouns.

Word	Noun	Adjective	Verb	Adverb
family Paridae	Yes	No	No	No
bird family	Yes	No	No	No

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

family Paridae: titmice and chickadees
bird family: a family of warm-blooded egg-laying vertebrates characterized by feathers and forelimbs modified as wings

family Paridae (noun)	bird family (noun)
titmice and chickadees	a family of warm-blooded egg-laying vertebrates characterized by feathers and forelimbs modified as wings