What is the ruling on water splattering onto clothes from washing a garment that has an unknown impurity, or a garment suspected of being impure, and does the ruling differ if the change in the detached water is indistinguishable?

This sprinkled water is judged to be pure in all estimations, because the default state of things is purity until impurity is established with certainty. As Ibn 'Uthaymeen said: "The default is for things to remain as they were. If one doubts the impurity of something pure, it remains pure. Or if one doubts the purity of something impure, it remains impure, because the default is for things to remain as they were." And as Al-Nawawi said: "Things are judged to remain in their original state until the contrary is certain. A sudden doubt does not harm them."

If a garment is doubted to be impure, it remains in its original state of purity. Consequently, the water separating from it is, even more so, pure. If its impurity is known but its specific location on the garment is unknown, this means it is a legal impurity (najasah hukmiyyah). A legal impurity is sufficiently purified by submerging the item in water. If water separates from the garment after its purification, it is considered pure. The inability to discern any change in the water serves as an indication of its soundness from alteration.

Therefore, you are not required to wash whatever of the aforementioned water touched you.