tool case vs tool chest

tool case and tool chest both are nouns.

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

As nouns, tool case and tool chest are synonyms defined as:

tool case and tool chest: a box or chest or cabinet for holding hand tools

Other synonyms of tool case include tool cabinet, toolbox.

tool case (noun)	tool chest (noun)
a box or chest or cabinet for holding hand tools	a box or chest or cabinet for holding hand tools