tool case vs chest

tool case and chest both are nouns.

Word	Noun	Adjective	Verb	Adverb
tool case	Yes	No	No	No
chest	Yes	No	No	No

As nouns, chest is a hypernym of tool case; that is, chest is a word with a broader meaning than tool case:

tool case (noun)	chest (noun)
a box or chest or cabinet for holding hand tools	box with a lid; used for storage; usually large and sturdy
	furniture with drawers for keeping clothes
	the part of the human torso between the neck and the diaphragm or the corresponding part in other vertebrates
	the front of the trunk from the neck to the abdomen