auto race vs automobile race

auto race and automobile race both are nouns.

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

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

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

Other synonyms of auto race include car race.

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