Taffeta is a specific weave and can be woven out of a myriad of fibers. A weave is defined by the pattern of over and unders the threads makes. Satin is again, a specific weave with certain characteristics and can be woven out of a lot of fabrics. Because of it's shiny appearance it is usually not women with "fuzzy" threads like wool or cotton. Silk is the extreme high end for satin and is to absolutely drool over.
Crushed taffeta is a taffeta that has been treated to be wrinkled on the bolt. It seems to be all the rage in fashion and accessories right now but like all fads will pass away. Taffeta, however, is almost as old as dirt and appears to be staying around for a while.