toy dog vs domestic dog

toy dog and domestic dog both are nouns.

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

As nouns, domestic dog is a hypernym of toy dog; that is, domestic dog is a word with a broader meaning than toy dog:

toy dog: any of several breeds of very small dogs kept purely as pets
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 hypernyms of toy dog include Canis familiaris, dog.

toy dog (noun)	domestic dog (noun)
any of several breeds of very small dogs kept purely as pets	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