Satin is a weave. Modal is a fibre.
This is the confusion the whole market is built on. Satin is a weave structure: a way of interlacing yarn so that most of it floats along the surface of the cloth rather than crossing over and under at every thread. That is what makes satin smooth and lustrous, and it is a property of the weave, not of any one material.
Modal is what we weave it from: a regenerated cellulose fibre made from beech wood pulp. You can weave satin out of silk, modal, viscose, polyester or nylon. So “satin pillowcase” tells you how it was woven and nothing about what it is made of — which is exactly why the word is used so freely.