Original Ideas are Fragile Things

I generally prefer novels to short story collections, but I would read a shopping list if Gaiman penned it.
I received Neil Gaiman’s collection of short stories Fragile Things for Christmas, and I’ve been devouring it rapidly. My favorite so far has been a gem called “Other People.”
The story details a man’s punishment in Hell, where he is physically tortured by a demon. He’s then forced to recount his life aloud again and again, admitting to every bad thing he’s ever done, and then he’s forced to learn the repercussions of his selfishness on other people.
In the end, the torture has left him looking like the demon, a soulless husk, and a new wayward human enters the chamber. The cycle begins anew.
In the forward, Gaiman recounts the doubt he felt upon completion of the story. It felt too circular, too neat to be original. It nagged at the back of his mind. He was sure it must have been a story he’d heard years before and then forgotten. After reading “Other People” to a number of friends, however, no one could name a derivative work.
I think this is a problem all writers face. Whenever I get an idea for a story, if I don’t get it written within a day or two, I usually talk myself out of it. I tell myself it’s too much like this other story or it’s taking too much from this movie.
Art doesn’t exist in a vacuum – everybody draws from their role models and inspirations. What separates us from them, though? How do we differentiate our work, and how do we mark that difference between being inspired by an artist and stealing from them?