You are correct, satin is a type of weave. It can be woven of any kind of fibre.Tabby weave- the warp (longways) threads cross over and under the weft (sideways) threads singly.
Twill weave- the weft threads cross over and under warp threads in groups. In this diagram, the threads are grouped in twos. Each row is offset from the row above and below to produce the characteristic twill pattern.
Satin weave- Weft threads pass over many warp threads before crossing under. In this example, the weft threads pass over 5 warp threads before passing under a warp thread.
Because of the long surface "runs" or amount of exposed, uncrossed thread, satin has a smooth finish. The effect is enhanced when a shiney fibre like silk is used.
It can be woven in any fibre- linen, cotton, silk, wool, etc.
Gwen