free living vs life-style

free living and life-style both are nouns.

Word	Noun	Adjective	Verb	Adverb
free living	Yes	No	No	No
life-style	Yes	No	No	No

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

free living: a lifestyle given to easy indulgence of the appetites
life-style: a manner of living that reflects the person's values and attitudes

Other hypernyms of free living include life style, lifestyle, modus vivendi.

free living (noun)	life-style (noun)
a lifestyle given to easy indulgence of the appetites	a manner of living that reflects the person's values and attitudes