auto tire vs automobile tire

auto tire and automobile tire both are nouns.

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

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

auto tire and automobile tire: a tire consisting of a rubber ring around the rim of an automobile wheel

Other synonyms of auto tire include car tire, rubber tire.

auto tire (noun)	automobile tire (noun)
a tire consisting of a rubber ring around the rim of an automobile wheel	a tire consisting of a rubber ring around the rim of an automobile wheel