Silk is a natural fabric. Satin is NOT a fabric, but rather a FINISH or WEAVE that can be use on almost ANY synthetic or natural fabric. Natural fabrics include cotton, silk, wool, etc. Synthetic fabrics include polyester, nylon, rayon, etc.
Satin is very tightly woven finish which provides one of the smoothest, seamless finish to most fabrics (chiffon is also a very smooth finish or weave, and NOT a fabric).
Thus, you can have a satin cotton, satin silk, satin polyester, etc.
Silk can have a variety of "finishes" from a smooth seamless satin finish to a rough texture 100 woven silk sweater -- all silks are NOT necessarily smooth textured -- it depends on the weave/finish.
I find that satin silks don't stay on my head at night because they're too "slippery" but satin polyesters or chiffon polyesters do a great job. IMO, as long as the FINISH is smooth and seamless (look for "satin" or "chiffon" finishes), your hair is gonna be fine. I tried the satin silks and just can't keep them on, plus, they're expensive to buy AND maintain -- most of the satin silks have to dry cleaned, whereas my satin polyesters can be hand washed and are waaaay cheaper. Unfortunately, a lot on-line retailers just say "satin" and DON'T make the distinction between FABRIC and FINISH and I have to call and ask what kind of FABRIC is it? If they can't tell me, I don't buy.
I hope this helps clear some of the confusion between "satin" and "silk". . .