Silk is a natural material that makes lightweight, breathable, temperature-regulating, and undeniably soft sheets. Satin isn't a material, but a pattern of weaving. That's what gives it the smooth, shiny appearance on the top and a duller finish on the back. Satin is made using fibers from fabrics like silk, nylon, and polyester.
If budget is no concern, silk sheets are the more luxurious pick.