packing box vs packing case

packing box and packing case both are nouns.

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

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

packing box and packing case: a large crate in which goods are packed for shipment or storage

packing box (noun)	packing case (noun)
a small chamber in which packing is compressed around a reciprocating shaft or piston to form a seal	a large crate in which goods are packed for shipment or storage
a large crate in which goods are packed for shipment or storage