lack vs shortage

lack and shortage both are nouns.

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

As nouns, shortage is a hyponym of lack; that is, shortage is a word with a more specific, narrower meaning than lack:

Other hyponyms of lack include absence, dearth, famine, deficit, mineral deficiency, shortness, stringency, tightness.

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

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