natural state vs state of nature

natural state and state of nature both are nouns.

Word	Noun	Adjective	Verb	Adverb
natural state	Yes	No	No	No
state of nature	Yes	No	No	No

As nouns, natural state and state of nature are synonyms defined as:

natural state and state of nature: a wild primitive state untouched by civilization

Other synonyms of natural state include wild.

natural state (noun)	state of nature (noun)
a wild primitive state untouched by civilization	a wild primitive state untouched by civilization