What is the difference between sprinkling (nadh) and washing (ghusl), and what is added in ghusl beyond pouring water, especially given the mention of "sprinkling" (nadh) in the hadith about the urine of a boy and "washing" (ghusl) in the hadith about the urine of a girl?

The difference between nadh (sprinkling) and ghusl (washing) is that nadh is merely sprinkling water on the site of impurity such that it covers it without flowing or dripping, whereas ghusl is the flowing of water over the item such that it covers it and flows and drips from it. It is not necessary to wring the impure spot during ghusl unless the removal of the impurity depends on it.