house cat vs true cat

house cat and true cat both are nouns.

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

As nouns, true cat is a hypernym of house cat; that is, true cat is a word with a broader meaning than house cat:

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

Other hypernyms of house cat include domestic animal, domesticated animal, cat.

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