I think that ALL these terms, washing, redeeming and the rest are all images of the one thing. I think drawing “bright lines” between these aspects of the Atonement can tangle us up.
Satisfaction, expiatory sacrifice, conquering our ancient adversary, manifesting the truth of the Love of God — all these, in my alleged thought, are not different things but one Atonement understood from different approaches.
So here, blood pays the blood debt, there it covers our death-dealing sin with the blood which is life, over there it is a tide which sweeps death and Satan away, and then it is also the revelation of the depths of the Love of God in Jesus, a love so great that even after death blood and water are shed on us.
That's how I'd work it, anyway.
I tend to agree, but even though our sins are forgiven, they are without consequence. There is a price to be paid and it was paid by Jesus. Those who believe that they can act with complete impunity in their actions today because the sacrifice of Jesus secured their elect or "saved" status are wrong.