automobile race vs car race

automobile race and car race both are nouns.

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

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

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

Other synonyms of automobile race include auto race.

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