In actual practice, short field and soft field turn out to be the same thing, most of the time. Short fields are often soft, and soft fields are seldom long. The method provided for most private pilot training for short fields involves holding brakes and applying takeoff power...something sure to suck up rocks and damage airplanes in the real world, and seldom applicable to short/soft field operations.
In either case, short or soft, the goal is the same; get the airplane into the air and off the surface as soon as possible, and one must always be mindful of obstacles.