This is the most common confusion in the category, and it is a labelling problem before it is a product problem.
What satin actually is
Satin is a weave structure. The warp yarns float over several weft yarns before going under one, which puts most of the yarn on the surface and produces that smooth light-catching face.
You can weave satin from polyester, viscose, nylon or silk. The weave says nothing at all about the fibre.
What silk is
A natural protein fibre from the silkworm. It is smoother than almost anything, it regulates temperature, it costs a great deal more, and it needs gentler washing.
Silk can be woven as satin, as charmeuse, as habotai or as anything else. The fibre says nothing about the weave either.
Why the distinction is worth keeping
Polyester satin is a genuinely good scrunchie. It is smooth against hair, durable, inexpensive and it survives a washing machine, which real silk resents.
The problem is only ever the labelling. A customer who paid a silk price for a polyester product finds out eventually, and what they remember is the shop rather than the supplier.
What to put on your packaging
The fibre and the weave, separately and plainly: “polyester satin”, or “100% mulberry silk”. Add the care instruction.
It costs nothing, it removes an entire category of complaint, and in a market where everybody else is being vague it reads as confidence.