gear case vs gear box

gear case and gear box both are nouns.

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

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

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

Other synonyms of gear case include gearbox.

gear case (noun)	gear box (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