sabertooth vs big cat

sabertooth and big cat both are nouns.

Word	Noun	Adjective	Verb	Adverb
sabertooth	Yes	No	No	No
big cat	Yes	No	No	No

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

sabertooth: any of many extinct cats of the Old and New Worlds having long swordlike upper canine teeth; from the Oligocene through the Pleistocene
big cat: any of several large cats typically able to roar and living in the wild

Other hypernyms of sabertooth include cat.

sabertooth (noun)	big cat (noun)
any of many extinct cats of the Old and New Worlds having long swordlike upper canine teeth; from the Oligocene through the Pleistocene	any of several large cats typically able to roar and living in the wild