story vs life history

story and life history both are nouns.

Word	Noun	Adjective	Verb	Adverb
story	Yes	No	No	No
life history	Yes	No	No	No

As nouns, life history is a hyponym of story; that is, life history is a word with a more specific, narrower meaning than story:

story (noun)	life history (noun)
a structure consisting of a room or set of rooms at a single position along a vertical scale	the general progression of your working or professional life
a piece of fiction that narrates a chain of related events	an account of the series of events making up a person's life
a short account of the news
a trivial lie
a message that tells the particulars of an act or occurrence or course of events; presented in writing or drama or cinema or as a radio or television program
a record or narrative description of past events