Satin, Charmeuse and Mulberry Silk are three totally different concepts.
Satin is a weave
Satin is a weave that typically has a glossy surface and a dull back. The satin weave is characterized by four or more fill or weft yarns floating over a warp yarn or vice versa, four warp yarns floating over a single weft yarn. Floats are missed interfacings, where the warp yarn lies on top of the weft in a warp-faced satin and where the weft yarn lies on top of the warp yarns in weft-faced satins. If a fabric is formed with a satin weave using filament fibres such as silk, nylon, or polyester, the corresponding fabric is termed a satin.
Charmeuse is a fabric, made of silk or Synthetic fibers
Charmeuse is a lightweight fabric woven with a satin weave, in which the warp threads cross over three or more of the backing (weft) threads. These float threads give the front of the fabric a smooth finish—lustrous and reflective—whereas the back has a dull finish. It can be made of silk or a synthetic lookalike such as polyester.
Mulberry Silk is Natural fiber
Mulberry silk is spun from the natural silk protein filament produced by the silk worm when forming its cocoon. Mulberry silk is the most common among the many kinds of silk. It makes up 90% of the silk supply in the world.