barking deer vs deer

barking deer and deer both are nouns.

Word	Noun	Adjective	Verb	Adverb
barking deer	Yes	No	No	No
deer	Yes	No	No	No

As nouns, deer is a hypernym of barking deer; that is, deer is a word with a broader meaning than barking deer:

barking deer: small Asian deer with small antlers and a cry like a bark
deer: distinguished from Bovidae by the male's having solid deciduous antlers

Other hypernyms of barking deer include cervid.

barking deer (noun)	deer (noun)
small Asian deer with small antlers and a cry like a bark	distinguished from Bovidae by the male's having solid deciduous antlers