health vs welfare

health and welfare both are nouns.

Word	Noun	Adjective	Verb	Adverb
health	Yes	No	No	No
welfare	Yes	No	No	No

As nouns, welfare is a hypernym of health; that is, welfare is a word with a broader meaning than health:

Other hypernyms of health include eudaemonia, eudaimonia, upbeat, well-being, wellbeing.

health (noun)	welfare (noun)
a healthy state of wellbeing free from disease	governmental provision of economic assistance to persons in need
the general condition of body and mind	something that aids or promotes well-being
	a contented state of being happy and healthy and prosperous