Your response is closest to my own definition. I generally think of a set of steps as outside (and solid, like concrete, brick, or stone) and stairs as indoor (and made of wood). But there are exceptions in the way I use the words. For instance, I might say "the bottom step" even if I'm talking about one of a set of indoor wooden stairs. Or I might say "stair;" I feel like they're interchangeable in that case. If there's a flight of stone stairs indoors, like in a mall, I might call it steps. But I think I would call outdoor wooden steps "steps," not stairs.