shortage vs lack

shortage and lack both are nouns.

Word	Noun	Adjective	Verb	Adverb
shortage	Yes	No	No	No
lack	Yes	No	Yes	No

As nouns, lack is a hypernym of shortage; that is, lack is a word with a broader meaning than shortage:

Other hypernyms of shortage include deficiency, want.

shortage (noun)	lack (noun)
the property of being an amount by which something is less than expected or required	the state of needing something that is absent or unavailable
an acute insufficiency

shortage (verb)	lack (verb)
	be without
	To be insufficiently prepared