detective story vs mystery

detective story and mystery both are nouns.

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

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

detective story: a narrative about someone who investigates crimes and obtains evidence leading to their resolution
mystery: a story about a crime (usually murder) presented as a novel or play or movie

Other hypernyms of detective story include mystery story, whodunit.

detective story (noun)	mystery (noun)
a narrative about someone who investigates crimes and obtains evidence leading to their resolution	something that baffles understanding and cannot be explained
	a story about a crime (usually murder) presented as a novel or play or movie