cheetah vs big cat

cheetah and big cat both are nouns.

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

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

cheetah: long-legged spotted cat of Africa and southwestern Asia having nonretractile claws; the swiftest mammal; can be trained to run down game
big cat: any of several large cats typically able to roar and living in the wild

Other hypernyms of cheetah include cat.

cheetah (noun)	big cat (noun)
long-legged spotted cat of Africa and southwestern Asia having nonretractile claws; the swiftest mammal; can be trained to run down game	any of several large cats typically able to roar and living in the wild