To echo Ang and Nicole - velvet is a weave, satin is a different weave, so it can't be both. When describing a fabric you can describe the weave (or knit) which is how it's made, and then the fiber content, which is what it's actually made from (cotton, silk, wool, polyester, etc). When you do a burn test you are testing for fiber content.
I'm having a hard time making out what's going on with the designs on the outside of the skirt from the pictures:
Are they raised? (If they are raised and sort of velvety while the background is smooth and silky, maybe this is a flocked piece, if it's embroidery or woven threads that are raised up a bit from the background, maybe it's a brocade or jacquard.)
Places where the velvet pile has been pressed flat? (That would be embossed velvet.)
Or places where the velvet pile is gone? (That would be voided or etched velvet.)
The "pile" is the soft tufts of fabric that stick up and its fiber content is often something like rayon, cotton, acetate (really common now), polyester and (very, very rarely anymore) silk.
The backing is the fabric that the pile is attached to. Its fiber content is often something like rayon, cotton, silk, acetate or other synthetics.
The pile and backing can be the same fiber, like cotton velvet often is, or different fibers.