pencil case vs pencil box

pencil case and pencil box both are nouns.

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

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

pencil case (noun)	pencil box (noun)
a box for holding pencils	a box for holding pencils