lapdog vs domestic dog

lapdog and domestic dog both are nouns.

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

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

lapdog: a dog small and tame enough to be held in the lap
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 lapdog include Canis familiaris, dog.

lapdog (noun)	domestic dog (noun)
a dog small and tame enough to be held in the lap	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