motorway vs state highway

motorway and state highway both are nouns.

Word	Noun	Adjective	Verb	Adverb
motorway	Yes	No	No	No
state highway	Yes	No	No	No

As nouns, motorway and state highway are synonyms defined as:

motorway and state highway: a broad highway designed for high-speed traffic

Other synonyms of motorway include expressway, freeway, pike, superhighway, throughway, thruway.

motorway (noun)	state highway (noun)
a broad highway designed for high-speed traffic	a broad highway designed for high-speed traffic