How did the twentieth-century American mystery story evolve in a very different direction than the British version?

The twentieth-century American mystery story evolved away from the gentle "cosy" traditional of British mysteries towards what is called the "hard-boiled" crime genre. This reflects the different character and historical moment of the two nations.
Twentieth-century British mysteries tend to be set in the countryside, often at a large and wealthy country home with many servants. They are concerned with preserving the status quo and reinstating moral order when chaos threatens. As the British mystery writer P.D. James expresses it, British mysteries are conservative, interested in “bringing order out of disorder. She calls the mysteries part of “a genre of reconciliation and social healing." The genre thus reflects the class system that was and is part of British life.
The backward-looking view of the British mystery also reveals nostalgia for the country's "glory days" of the nineteenth-century and the Edwardian period, before the First World War. A large number of these mysteries take place in the kinds of homes that were fast disappearing in the twentieth-century, reflecting a wealth and power that was only a memory to many Britons.
Meanwhile, the American mystery novel was evolving to reflect the ethos of a brash, rising nation. Many of the most famous novels are set in big, corrupt cities like Los Angeles. Rather than affirming the moral order, as British mysteries did, American hardboiled mysteries emphasize pervasive corruption: anyone can be a criminal or murderer and crime is imbedded in the fabric of life. The US is a country where people do what they can to get ahead. Detectives like Chandler's Sam Spade are not primarily concerned with moral issues. In The Maltese Falcon, Spade states that he arrests would-be criminals not because they are necessarily guilty, but because it's his job and in his nature:

I’m a detective and expecting me to run criminals down and then let them go free is like asking a dog to catch a rabbit and let it go. It can be done, all right, and sometimes it is done, but it’s not the natural thing.

If British mysteries of the prior century were characterized by the soft, pastoral glow of a country estate, emphasizing that the world is a good place except for the unusual entrance of a crime, the colors and feel of an American hard-boiled mystery are hard and stark, characterized by the neon lights and modern apartment buildings of new America.
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https://seonaidhceanneidigh.wordpress.com/2014/07/11/the-roots-of-american-british-crime-fiction/