packing case vs crate

packing case and crate both are nouns.

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

As nouns, crate is a hypernym of packing case; that is, crate is a word with a broader meaning than packing case:

packing case: a large crate in which goods are packed for shipment or storage
crate: a rugged box (usually made of wood); used for shipping

packing case (noun)	crate (noun)
a large crate in which goods are packed for shipment or storage	a rugged box (usually made of wood); used for shipping
	the quantity contained in a crate

packing case (verb)	crate (verb)
	put into a crate; as for protection