true cat vs house cat

true cat and house cat both are nouns.

Word	Noun	Adjective	Verb	Adverb
true cat	Yes	No	No	No
house cat	Yes	No	No	No

As nouns, house cat is a hyponym of true cat; that is, house cat is a word with a more specific, narrower meaning than true cat:

true cat: feline mammal usually having thick soft fur and no ability to roar: domestic cats; wildcats
house cat: any domesticated member of the genus Felis

Other hyponyms of true cat include domestic cat, Felis catus, Felis domesticus, wildcat.

true cat (noun)	house cat (noun)
feline mammal usually having thick soft fur and no ability to roar: domestic cats; wildcats	any domesticated member of the genus Felis