toolbox vs tool chest

toolbox and tool chest both are nouns.

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

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

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

Other synonyms of toolbox include tool cabinet, tool case.

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