Often the two overlap. However, pure crime films/novels focus on a specific crime or set of crimes, and solving the mystery or tracking down the criminal(s), with no or little violence but more drama throughout. Thrillers are usually fiction-based and fast in pace, while crime fiction tend to be more leisurely paced, dramatic and realistic. Generally, violence is also lacking in a crime fiction, but this depends if the work is based on the mafia, where violence is intense.
Some crime films showcase more on the gangster life, personal drama of the criminals and even their biographical film (i.e., The Godfather). Crime-thrillers, on the other hand, have more threat and suspense in them and may involve espionage (spying), frequent killings and other non-criminal conflicts (i.e., Heat). Unlike crime thrillers, crime films usually offer a more serious, grim and realistic portrayal of the criminal environment, emphasizing character development and complex narratives over suspense sequences, chase scenes and violence.
In crime fiction, the hero might be a police officer, or a private eye, who can still be tough and resourceful. He is pitted against villains determined to destroy him, although, unlike in thrillers, not necessarily other people, the country or the stability of the free world. Unlike in crime fiction, thrillers keep the emphasis away from the gangster, melodrama or the detective in the crime-related plot, and rather focus more on the suspense and danger that is generated.