story vs short story

story and short story both are nouns.

Word	Noun	Adjective	Verb	Adverb
story	Yes	No	No	No
short story	Yes	No	No	No

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

story (noun)	short story (noun)
a structure consisting of a room or set of rooms at a single position along a vertical scale	a prose narrative shorter than a novel
a piece of fiction that narrates a chain of related events
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