lumber jacket vs lumberjack

lumber jacket and lumberjack both are nouns.

Word	Noun	Adjective	Verb	Adverb
lumber jacket	Yes	No	No	No
lumberjack	Yes	No	No	No

As nouns, lumber jacket and lumberjack are synonyms defined as:

lumber jacket (noun)	lumberjack (noun)
a short warm outer jacket	a short warm outer jacket
	a person who fells trees