natural order vs existence

natural order and existence both are nouns.

Word	Noun	Adjective	Verb	Adverb
natural order	Yes	No	No	No
existence	Yes	No	No	No

As nouns, existence is a hypernym of natural order; that is, existence is a word with a broader meaning than natural order:

natural order: the physical universe considered as an orderly system subject to natural (not human or supernatural) laws
existence: everything that exists anywhere

Other hypernyms of natural order include cosmos, creation, macrocosm, universe, world.

natural order (noun)	existence (noun)
the physical universe considered as an orderly system subject to natural (not human or supernatural) laws	everything that exists anywhere
	the state or fact of existing