fireman vs fire fighter

fireman and fire fighter both are nouns.

Word	Noun	Adjective	Verb	Adverb
fireman	Yes	No	No	No
fire fighter	Yes	No	No	No

As nouns, fireman and fire fighter are synonyms defined as:

fireman and fire fighter: a member of a fire department who tries to extinguish fires

Other synonyms of fireman include fire-eater, firefighter.

fireman (noun)	fire fighter (noun)
play in which children pretend to put out a fire	a member of a fire department who tries to extinguish fires
a member of a fire department who tries to extinguish fires
a laborer who tends fires (as on a coal-fired train or steamship)
a pitcher who does not start the game