What’s the difference between purity and righteousness?
Your question is very short, and thus it is hard to discern your intent. Forgive me if I have misunderstood you. At first glance, some might say there is no difference. However, a very cursory search on LDS.org for “purity” brings up several articles about keeping the Law of Chastity. Righteousness is generally thought of in a more broad sense. However, it is understood that if one wants to be righteous, they will also be morally clean and pure. In that sense, they are the same.
Some survivors of sexual abuse and rape may struggle with these concepts feeling that they are “unclean” because of what happened to them. Blaming oneself is very common among survivors, even when their own logic denies the possibility, the feeling can be very strong. But it is not their fault.
Elder Holland once said speaking of immorality, “One who uses the God-given body of another without divine sanction abuses the very soul of that individual, abuses the central purpose and processes of life.” Personal Purity
He was speaking to couples in which both parties are consenting. How much stronger would his language surely be if he was speaking to those who force themselves on another person?
I would like to tell all survivors of sexual abuse or rape, it wasn’t your fault. You are clean. You are pure. You are righteous. No one else’s actions can take that away from you.