life eternal vs living

life eternal and living both are nouns.

Word	Noun	Adjective	Verb	Adverb
life eternal	Yes	No	No	No
living	Yes	Yes	No	No

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

Other hypernyms of life eternal include aliveness, animation, life.

life eternal (noun)	living (noun)
life without beginning or end	the experience of being alive; the course of human events and activities
	people who are still living
	the financial means whereby one lives
	the condition of living or the state of being alive

life eternal (adjective)	living (adjective)
	pertaining to living persons
	(informal) absolute
	still in existence
	(used of minerals or stone) in its natural state and place; not mined or quarried
	true to life; lifelike
	still in active use