state trooper vs trooper

state trooper and trooper both are nouns.

Word	Noun	Adjective	Verb	Adverb
state trooper	Yes	No	No	No
trooper	Yes	No	No	No

As nouns, state trooper and trooper are synonyms defined as:

state trooper (noun)	trooper (noun)
a state police officer	a mounted police officer
	a soldier in a motorized army unit
	a state police officer
	a soldier mounted on horseback