living wage vs wage

living wage and wage both are nouns.

Word	Noun	Adjective	Verb	Adverb
living wage	Yes	No	No	No
wage	Yes	No	Yes	No

As nouns, wage is a hypernym of living wage; that is, wage is a word with a broader meaning than living wage:

living wage: a wage sufficient for a worker and family to subsist comfortably
wage: something that remunerates

Other hypernyms of living wage include earnings, pay, remuneration, salary.

living wage (noun)	wage (noun)
a wage sufficient for a worker and family to subsist comfortably	something that remunerates

living wage (verb)	wage (verb)
	carry on (wars, battles, or campaigns)