Skiing different terrain requires different equipment.
Off piste skis differ slightly to traditional piste skis, whereby they are typically wider, have a greater rocker at the front as well as different types of camber to assist with the varying terrain (powder, ice, crust, as well as slope angle).
Bindings are fairly similar, unless you are doing any ski touring in which case the bindings will be quite different (pin bindings).
Likewise with the boots; they are fairly similar, however some off piste boots will have a ‘walk mode’. If you are doing ski touring then the boots will have a walk mode as well as ‘pin inserts’ to allow for the pivoting movement.
Poles may have wider baskets so that they don’t sink in powder.
Depending on the course, ice axe, harness, rope, ice screws and crampons may be required.