It is always difficult to pigeonhole any genre (the best stories usually being those that break all the definitions) and SFF is even harder to categorize as we have frequently found in threads on this forum, because science fiction means different things to different people. Personally I would compare The Twilight Zone to Ray Bradbury stories. Now, they are are found in the Science Fiction shelves of bookshops, but Bradbury himself said that he didn't write science fiction, and that he had only ever written one science fiction story (which I take to be Fahrenheit 451, but maybe he meant something else.) So, he clearly thought he wrote Fantasy. Certainly The Twilight Zone has elements of supernatural, but then so does The X-Files or Warehouse 13 or a good many other supposed SF shows . Maybe it is "whatever you want it to be."