murder mystery vs mystery story

murder mystery and mystery story both are nouns.

Word	Noun	Adjective	Verb	Adverb
murder mystery	Yes	No	No	No
mystery story	Yes	No	No	No

As nouns, mystery story is a hypernym of murder mystery; that is, mystery story is a word with a broader meaning than murder mystery:

murder mystery: a narrative about a murder and how the murderer is discovered
mystery story: a story about a crime (usually murder) presented as a novel or play or movie

Other hypernyms of murder mystery include mystery, whodunit.

murder mystery (noun)	mystery story (noun)
a narrative about a murder and how the murderer is discovered	a story about a crime (usually murder) presented as a novel or play or movie