tool chest vs tool case

tool chest and tool case both are nouns.

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

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

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

Other synonyms of tool chest include tool cabinet, toolbox.

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