story vs urban legend

story and urban legend both are nouns.

Word	Noun	Adjective	Verb	Adverb
story	Yes	No	No	No
urban legend	Yes	No	No	No

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

story: a short account of the news
urban legend: a story that appears mysteriously and spreads spontaneously in various forms and is usually false; contains elements of humor or horror and is popularly believed to be true

Other hyponyms of story include newsletter, newssheet, bulletin, communique, despatch, dispatch, exclusive, scoop.

story (noun)	urban legend (noun)
a structure consisting of a room or set of rooms at a single position along a vertical scale	a story that appears mysteriously and spreads spontaneously in various forms and is usually false; contains elements of humor or horror and is popularly believed to be true
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