The situation with collected editions of Somerset Maugham's short stories is complex.
Complete Short Stories have been published in three volumes (Heinemann, 1951), in two volumes (Doubleday, 1952: I. East and West; II: The World Over) and even in four volumes (Washington Square Press, 1967). In contrast, Collected Short Stories have been published only in four volumes, first by Penguin in 1963, later by many other publishers (Pan, Mandarin, Folio Society, Vintage).
All of these editions, regardless of the number of volumes, contain the same 91 short stories. Therefore they all belong to this work, even though the Heinemann and the Doubleday editions contain two very different sets of prefaces by Maugham.
Please do not combine with separate volumes from any of these multivolume sets (e.g. East and West, Altogether* or The World Over), nor with any other single-volume collections. There is no one-volume edition of Maugham's short stories to approach such state of completeness as any of the multi-volume sets does.
*English title of what was published in the USA as East and West.