car race vs automobile race

car race and automobile race both are nouns.

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

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

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

Other synonyms of car race include auto race.

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