Lucy says that she "put a little dishwashing detergent on" a "sponge" to clean the dishes. Detergent, "detergent," is another word for soap, a special kind of soap. In this case, it's soap for washing dishes, so it's dishwashing detergent -dishwashing soap - it's the same. You can also have detergent to wash your clothes, so the special soap you use to wash your clothes in a machine would be called detergent.
n. 清洁剂
adj. 用于清洗的