race car vs auto

race car and auto both are nouns.

Word	Noun	Adjective	Verb	Adverb
race car	Yes	No	No	No
auto	Yes	No	No	No

As nouns, auto is a hypernym of race car; that is, auto is a word with a broader meaning than race car:

race car: a fast car that competes in races
auto: a motor vehicle with four wheels; usually propelled by an internal combustion engine

Other hypernyms of race car include automobile, car, machine, motorcar.

race car (noun)	auto (noun)
a fast car that competes in races	a motor vehicle with four wheels; usually propelled by an internal combustion engine