natural history vs science

natural history and science both are nouns.

Word	Noun	Adjective	Verb	Adverb
natural history	Yes	No	No	No
science	Yes	No	No	No

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

natural history: the scientific study of plants or animals (more observational than experimental) usually published in popular magazines rather than in academic journals
science: a particular branch of scientific knowledge

Other hypernyms of natural history include scientific discipline.

natural history (noun)	science (noun)
the scientific study of plants or animals (more observational than experimental) usually published in popular magazines rather than in academic journals	a particular branch of scientific knowledge
	ability to produce solutions in some problem domain