mongrel vs pye-dog

mongrel and pye-dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
mongrel	Yes	No	No	No
pye-dog	Yes	No	No	No

As nouns, pye-dog is a hyponym of mongrel; that is, pye-dog is a word with a more specific, narrower meaning than mongrel:

mongrel: an inferior dog or one of mixed breed
pye-dog: ownerless half-wild mongrel dog common around Asian villages especially India

Other hyponyms of mongrel include feist, fice, pariah dog, pie-dog.

mongrel (noun)	pye-dog (noun)
an inferior dog or one of mixed breed	ownerless half-wild mongrel dog common around Asian villages especially India
derogatory term for a variation that is not genuine; something irregular or inferior or of dubious origin