A crime story can also be another name for a detective story. Detective stories usually revolve around crimes, and so do crime stories. They share many common elements such as the investigation process, the suspects, and the clues.
A mystery story. It often involves solving a crime or uncovering a secret, just like a detective story.
A sleuth story. 'Sleuth' is another word for a detective, so a sleuth story is essentially a detective story.
Well, another name could be a crime novel. Detective novels often revolve around solving crimes, and crime novels have a similar focus on criminal activities and the process of uncovering the truth behind them. They usually involve elements like a crime scene, suspects, and a protagonist, often a detective or someone with investigative skills, trying to piece together what really happened. So, crime novel is a valid alternative name.
A yarn can also be another name for a story. This term is often used in a more informal or folksy way. People might say 'spin a yarn' which means to tell a story, usually one that is interesting or perhaps a little exaggerated.
A noir story can be considered as another name in a sense. Noir stories often have a detective - like figure and involve elements of mystery and crime. They typically have a dark and moody atmosphere which is also common in many detective stories.
A chronicle. A chronicle is more like a record of events in the order in which they occurred. However, it can also be seen as a type of story, especially when it is told in a more engaging and narrative way, like historical chronicles that describe the lives of people and the events of a particular time period.