canine vs domestic dog

canine and domestic dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
canine	Yes	Yes	No	No
domestic dog	Yes	No	No	No

As nouns, domestic dog is a hyponym of canine; that is, domestic dog is a word with a more specific, narrower meaning than canine:

canine: any of various fissiped mammals with nonretractile claws and typically long muzzles
domestic dog: a member of the genus Canis (probably descended from the common wolf) that has been domesticated by man since prehistoric times; occurs in many breeds

Other hyponyms of canine include bitch, Canis familiaris, dog, wolf, jackal, wild dog, hyaena, hyena, fox.

canine (noun)	domestic dog (noun)
any of various fissiped mammals with nonretractile claws and typically long muzzles	a member of the genus Canis (probably descended from the common wolf) that has been domesticated by man since prehistoric times; occurs in many breeds
one of the four pointed conical teeth (two in each jaw) located between the incisors and the premolars

canine (adjective)	domestic dog (adjective)
of or relating to or characteristic of members of the family Canidae
of or relating to a pointed conical tooth