story vs love story

story and love story both are nouns.

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

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

story (noun)	love story (noun)
a structure consisting of a room or set of rooms at a single position along a vertical scale	a story dealing with love
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