Parah Adumah water: different names used in the Torah ("mei niddah") and Chazal ("mei chatas")

Question

When discussing the mixture of the Parah Adumah ashes & water, the Torah calls it "mei niddah" (see: Numbers 19:13, Numbers 19:20, Numbers 19:21).

However Chazal use a different phrase and refer to this water as "mei chatas" (see: Parah 5:5, Parah 6:5, Parah 8:2).

Why is there this difference of names in how to refer to the Parah Adumah water?

^{NOTE: This OU torah article says an answer can be found in Aruch Hashulchan Ha’atid, Taharot 76:8, the book on laws which will eventually come into use by author of the famed Aruch Hashulchan, but I don't have access to it.}

Answer 1

Rashi Bamidbar 19.9

"למי נדה" - למי הזייה כמו (איכה ג) וידו אבן בי (זכריה ב) לידות את קרנות הגוים לשון זריקה

"חטאת הוא" - לשון חטוי כפשוטו ולפי הלכותיו קראה הכתוב חטאת לומר שהיא כקדשים להאסר בהנאה

Nidda addresses the fact that the waters are throwed. Chatas addresses two thinks, the first according to the pshat, that the waters clean, the second, that the cow and the waters are prohibited from benefit as sacrifices.

I think the both names were from the beginning, each enhance one side. Since there is a lot of halachot derabanan regarding the uncleanness of the waters, see Mishna chagiga 2.7 for instance,

יוחנן בן גודגדא היה אוכל על טהרת הקודש כל ימיו, והיתה מטפחתו מדרס לחטאת

There are stringencies regarding chatas, is est waters of para aduma. regarding the special rules of tevila, the term regarding the halachot, chatos, is more used by Chazal