pencil box vs pencil case

pencil box and pencil case both are nouns.

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

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

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