Sin has two aspects according to Rav Joseph B. Soloveitchik – the sin itself which necessitates punishment and the stain it causes on the soul – even his halakhic personality changes.
The first aspect requires כפרה (atonement); the second aspect requires purification (טהרה).
This is why King David asks God not just for forgiveness but also to be purified (טהרני).
Ki Tavo 5778-The Essentials of Teshuva according to Rav Soloveitchik-Tehillim 51