Tazkiyah and Tasawwuf – Moosa Richardson
The term “tazkiyah” is from the verb “zak-kaa yuzak-kee” and the idea of making “tazkiyah of one’s nafs” is mentioned in the Qur’aan with two different ideas:
 Purifying one’s self (or others)from shirk, insincerity and/or disobedience. (see Soorah ash-Shams, an-Naazi’aat, ‘Abasa 2x, and al-A’laa for self-purification; for purifying others through teaching see: Soorah al-Jumu’ah the first verse and Aali Imraan:164)
 Claiming purity or piety, claiming that someone is “zakee” (see an-Najm: 32 – meaning “Do not claim that you are pure!” and Nisaa':49)
It is also used in the books of fiqh (and some angles of tafseer may support it from some verses) to refer to the payment of zakaat, fulaan yuzakkee i.e. somebody pays zakaat. This may be included in the general meaning of the first one above, since the payer of zakaat actually gets his wealth purified by the payment of the zakaat, and Allaah knows best.
So, in brief: a newsletter or or website called “tazkiyyah” is most likely claiming to pass on the teachings of the messenger of Allaah sallallaahu ‘alayhe wa sallam, teachings that purify people of impure beliefs and practices, so there is no problem in that name, in shaa’ Allaah.
As for the issue of “tasaw-wuf” then it comes from “fulaan tasaw-wafa ithaa labisa as-soof” somebody who does tasawwuf is someone who wears a woolen garment, so the people who live in cold places and wear wool jackets are mutasawwifoon, people who wear soof (wool). This was done in the early years of Islaam by ascetic Muslims who gave little concern for worldly possessions. Many of them were people of Sunnah upon the ‘aqeedah of the Messenger of Allaah (sallallaahu ‘alayhe wa sallam), nothing to do with what we call today “soofees” – sects of deviation differing from the creed of the Messenger (sallallaahu ‘alayhe wa sallam). They wore wool because there was little to no use for the material in hot climates and thus it was extremely cheap as a material or even free. As time went on, people who were ascetic commonly wore wool, and thus it took on a linguistic meaning that asceticism could be known by tasawwuf (the wearing of wool), and then the word tasawwuf became used to refer directly to indifference to wordly matters. It became a synonym for “zuhd” (asceticism, or indifference to or distace oneself from worldly pleasures).
So the scholars of Ahlus-Sunnah who praised someone for tasaw-wuf, they meant zuhd, not heretic beliefs, may Allaah bless you.
Now in later times, when a person leaves Ahlus-Sunnah and deviates into one of the Soofee cults, we say fulaan tasaw-wafa (taban-naa math-habas-soofiyyah), like we say tajah-hama when someone adopts the dogma of the jahmiyyah. I hope this provides some insight, and Allaah knows best.