domestic dog vs toy dog

domestic dog and toy dog both are nouns.

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

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

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
toy dog: any of several breeds of very small dogs kept purely as pets

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