gear case vs gearbox

gear case and gearbox both are nouns.

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

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

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

Other synonyms of gear case include gear box.

gear case (noun)	gearbox (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