auto race vs car race

auto race and car race both are nouns.

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

As nouns, auto race and car race are synonyms defined as:

auto race and car race: a race between (usually high-performance) automobiles

Other synonyms of auto race include automobile race.

auto race (noun)	car race (noun)
a race between (usually high-performance) automobiles	a race between (usually high-performance) automobiles