automobile race vs auto race

automobile race and auto race both are nouns.

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

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

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

Other synonyms of automobile race include car race.

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