Chihuahua vs toy dog

Chihuahua and toy dog both are nouns.

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

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

Chihuahua: an old breed of tiny short-haired dog with protruding eyes from Mexico held to antedate Aztec civilization
toy dog: any of several breeds of very small dogs kept purely as pets

Other hypernyms of Chihuahua include toy.

Chihuahua (noun)	toy dog (noun)
an old breed of tiny short-haired dog with protruding eyes from Mexico held to antedate Aztec civilization	any of several breeds of very small dogs kept purely as pets
the largest state in Mexico; mostly high plateau
a city in northern Mexico in the state of Chihuahua; commercial center of northern Mexico