You are asking about two different things in your original question and the clarification in your "Update 1".
An example that fits the criteria for your original question would be "Nightfall" by Isaac Asimov. This short story was expanded into a novel of the same name by Robert Silverberg.
Silverberg also expanded another of Asimov's stories, "The Bicentennial Man", into the novel "The Positronic Man" but I'm not sure whether Asimov was involved in the expansion. The novel was published in October 1992, half a year after Asimov died of AIDS (after having contracted HIV from a blood transfusion during a bypass surgery). In light of this timing, I conjecture that Asimov had little to know input in the expansion.
Another example, to a limited content is "Child of an Ancient City", which was written as a short story by Tad Williams and then expanded by Nina Kiriki Hoffman into a novel, albeit with Williams's involvement. Reportedly, Hoffman wrote the manuscript for the novel since Williams didn't have time to do that himself being in the middle of writing his "Memory, Sorrow, and Thorn" trilogy. Williams then edited it into its final form together with Hoffman.
I've also seen it many times in movies that the credits read something like "Screenplay by ABC, based on an idea by XYZ" but I can't give you an example right now.
All of these would not qualify as examples for what you ask for in your "Update 1".
Actually, the idea-to-screenplay examples look like they would qualify for both but in your original question you talk of "different authors/writers" implying that the original story was also produced by a writer which is incompatible with what you ask in your "Update 1".
Candidates for the second variety might be folk tales, fairy tales, legends, etc. that were put in writing at some point in time. The question would of course be whether there really was one original thinker and it will be impossible in many cases to know how vague their original concepts were.