gearbox vs gear case

gearbox and gear case both are nouns.

Word	Noun	Adjective	Verb	Adverb
gearbox	Yes	No	No	No
gear case	Yes	No	No	No

As nouns, gearbox and gear case are synonyms defined as:

gearbox and gear case: the shell (metal casing) in which a train of gears is sealed

Other synonyms of gearbox include gear box.

gearbox (noun)	gear case (noun)
the shell (metal casing) in which a train of gears is sealed	the shell (metal casing) in which a train of gears is sealed