The imagery is different, but the meaning is the same. In the process of preparing wool to become cloth or yarn, wool had to be washed to eliminate oils, dirt, and other impurities. Lye, a caustic substance often derived from wood ash, was used to bleach the wool in the washing process. The result was that white wool would become whiter (Mark 9:3). The meaning of our text is that God is like the soap that was used to wash the wool. God purifies his people, as described in the previous allusion to refining.
2 But who can endure the day of his coming, and who can stand when he appears? For he is like a refiner’s fire and like fullers’ soap.