While silk and satin are both soft and smooth materials, they are actually very different products. Silk is made only from natural fibres spun by silkworms. Satin, on the other hand, is a material that can be made from combinations of silk, polyester or nylon threads. Both satin and silk originated in China. The two materials are very versatile.
Look at the fabrics. Silk looks like it is shimmering. Satin, however, has a glossy appearance.
Look at the back of the fabric. Silk should have a shimmering appearance on both sides of the fabric. Satin, while glossy on one side appears dull on the back side.
Feel the fabric. Satin is more delicate than silk and needs better care. If you pull slightly at the fabric, you'll notice that satin moves easily but the silk has very little give.
Run your hand over the top of both fabrics. While both are smooth, silk feels much smoother than satin. Satin has a slightly rougher feel, though not by much.
Remember that satin can be made with silk threads. So if you see a satin that says there is silk in it, that is normal. It's just not a pure silk material.