Henry Kuttner & Catherine L. Moore were both prolific, and talented, writers who had established careers of their own before they married in 1940. After their marriage they frequently collaborated on stories, often published under pseudonyms, and it is claimed that their collaborations were so seamless that even the authors didn't know who had written what. It is even suggested that stories that were published under their solo names (particularly Kuttner's) were actually the work of both authors.Over the years since, these stories have been reprinted with a variety of attributions, with a single story sometimes appearing as by Kuttner alone, sometimes by Kuttner and Moore, and sometimes by Moore alone. Various attempts have been made to identify the precise author of each story, often with conflicting results, but the truth is that nobody really knows, or will ever know, quite who wrote what. An attempt has been made in these indexes to present a consistent picture of the authorship of each story, based on the best known evidence, but no claim is made for the accuracy of all such attributions.
For more information on the problems of untangling authorship of these stories, see the articles on Henry Kuttner in The Encyclopedia of Science Fiction and in Wikipedia.