Hand quilting thread has been coated with a wax to make it easier to work with. Do NOT use it in your machine because it will gum up the works.
Machine piecing thread is kind of a matter of choice. I use a 50 wt. cotton, I know people who use a polyester, etc. I would not use rayon embroidery thread to piece my quilt. I also don't really like the polyester wrapped cotton threads because they tend to shred. I've had to have my repairman remove some from between my machine's tension discs before. Expensive lesson.
Machine quilters like a wide variety of threads. I still wouldn't quilt with rayon embroidery thread but I guess art quilters might. There are many weights of thread. The higher the number the thinner the thread.