Assymetrical downwind sails
have a multitude of names and many of those names have been invented by specific sail lofts to identify their particular product, however, they're not necessarily product specific.
A spinnaker is a symmetrical sail flown off a pole and is most efficient when running deep off the wind
. Spinnakers can be used for reaching, but they're not at their best.
An assymetrical spinnaker (or gennaker, multi purpose sail (MPS), drifter, reacher, screacher, whatever) is generally flown off a strop off the bow of the boat (or off a prod at the bow of the boat) and is more efficient than a spinnaker for reaching but less efficient for sailing deep off the wind
. An assymetrical spinnaker can be flown off a pole in the same way as a symmetrical spinnaker is flown and that may allow you to sail deeper, however, its not going to be as efficient as a symmetrical spinnaker.