forest fire fighter vs fireman

forest fire fighter and fireman both are nouns.

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

As nouns, fireman is a hypernym of forest fire fighter; that is, fireman is a word with a broader meaning than forest fire fighter:

forest fire fighter: an official who is responsible for managing and protecting an area of forest
fireman: a member of a fire department who tries to extinguish fires

Other hypernyms of forest fire fighter include fire-eater, fire fighter, firefighter, functionary, official.

forest fire fighter (noun)	fireman (noun)
an official who is responsible for managing and protecting an area of forest	play in which children pretend to put out a fire
	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