suf = wool
safa' = purity
and while the former is more likely, the latter is given preference. The two were nicely combined by Abu `Ali al-Rudhabari (d. 322) who said:
al-sufi man labisa al-sufa `ala al-safa
The Sufi is the one who wears wool on top of purity.
Imam al-Suyuti cited it in his book on tasawwuf entitled Ta'yid al-Haqiqa al-`Aliyya wa-Tashyid al-Tariqa al-Shadhiliyya. At any rate these are the likelier etymologies mentioned by al-Qushayri, al-Huwjiri, Ibn Taymiyya, al-Shatibi, and many others. Not that etymological purity mattered at all to the Sufis. They couldn't care less.
In his major work entitled al-I`tisam on the definition of bid`a (innovation), al-Shatibi (d. 790) rejected the categorization of sufis and tasawwuf as an innovation in Islam according to his criteria.Sources:
2. As for the term "zahid" Imam Ahmad (d. 241) established that it applies first and foremost to the Prophet and his eminent Companions, ﷺ upon him blessings and peace and may Allah be well-pleased with them, and it applies as well to all the Prophets of Allah, peace upon them.
`Abd al-Qadir al-Baghdadi (d. 429) mentioned the two terms zahid and sufi interchangeably in his classifications of the groups that belong to Ahl al-Sunna wa al-Jama`a in his al-Farq bayn al-Firaq:
Know that Ahl al-Sunna wa al-Jama`a are divided in eight groups of people... the sixth group being the Sufi Ascetics (al-zuhhad al-sufiyya), who have seen things for what they are and therefore have abstained, who have known by experience and therefore have taken heed truly, who have accepted Allah's allotment and contented themselves with what is within reach.
3. The term "sufi" has been used in contrast with "faqih" (jurist) by the great Imams of Fiqh and Usul. It is enough that Imam al-Shafi`i  said:
faqihan wa sufiyyan fa kun laysa wahidan
fa inni wa haqqillahi iyyaka ansahu
Be both a faqih and a sufi: do not be only one of them!
Verily, by Allah's truth, I am advising you sincerely.
while Imam Malik  said:
man tasawwafa wa lam yatafaqqa fa qad tazandaqa
wa man tafaqqaha wa lam yatasawwaf fa qad tafassaqa
wa man jama`a bayn al-ithnayn fa qad tahaqqaqa
He who practices tasawwuf without learning Sacred Law
corrupts his faith, while he who learns Sacred Law without
practicing tasawwuf corrupts himself.
Only he who combines the two proves true.
- Al-Shafi`i, Diwan, (Beirut and Damascus: Dar al-fikr) p. 47.
- Imam Malik: see `Ali al-Qari, Sharh `Ayn al-`Ilm wa- Zayn al-Hilm (Cairo: Maktabat al-Thaqafa al-Diniyya, 1989) 1:33; Ahmad Zarruq, Qawa`id al-tasawwuf (Cairo, 1310); `Ali al-`Adawi, Hashiyat al-`Adawi `ala Sharh Abi al-Hasan li-Risalat Ibn Abi Zayd al-Musammat Kifayat al- Talib al-Rabbani li-Risalat Ibn Abi Zayd al-Qayrawani fi Madhhab Malik (Beirut?: Dar Ihya' al-Kutub al-`Arabiyah, (n.d.) 2:195; Ibn `Ajiba, Iqaz al-Himam fi Sharh al- Hikam (Cairo: Halabi, 1392/1972) p. 5-6.
4. Ibn al-Jawzi wrote a 100-page book on al-Hasan al- Basri's life and manners entitled Adab al-Shaykh al- Hasan ibn Abi al-Hasan al-Basri. In his chapter on al- Hasan in his compendium of the saints entitled Sifat al-Safwa -- based on Abu Nu`aym's Hilyat al-Awliya' -- Ibn al-Jawzi mentions a report that al-Hasan left behind a white cloak (jubba) made of wool (suf) which he had worn exclusively of any other for the past twenty years, winter and summer, and that when he died it was in a state of immaculate beauty, cleanness, and quality.
As to when Sufis formally appeared, then a "terminus ante quem" seems established with Hasan al-Basri (d. 110) and his student `Abd al-Wahid ibn Zayd (d. 177) who was the first person to build a Sufi khaniqa or guest-house and school at Abadan on the present-day border of Iran with Iraq.
This is related by the hafiz Abu Nu`aym (d. 430) and confirmed by Ahmad Ibn Taymiyya. Al-Harawi al-Ansari (d. 481) says in his Biographical Layers of the Sufi Masters that the first person to be actually named "al-Sufi" was Abu Hashim al-Sufi (d. 150?), a contemporary of Imam Sufyan al-Thawri (d. 165) who said: If it were not for Abu Hashim al-Sufi I would have never perceived the presence of the subtlest forms of hypocrisy in the self... Among the best of people is the Sufi learned in jurisprudence. 
Abu Nu`aym narrated it in Hilyat al-Awliya' and al-Harawi al-Ansari in his Tabaqat al-Sufiyya while Ibn al-Jawzi, who was violently allergic to the word "Sufi," names him Abu Hashim al-Zahid in his Sifat al-Safwa.
Sources: - Ibn al-Jawzi, Sifat al-Safwa 2(4):10 (#570) and 1(2):203 (#254).
- Abu Nu`aym, Hilyat al-Awliya' 6:155 and s.v. "Abu Hashim."
- Ibn Taymiyya, al-Sufiyya wal-Fuqara', beginning of volume 11 of his Majmu`at al-Fatawa al-Kubra entitled "al-tasawwuf."
- Al-Harawi al-Ansari, Tabaqat al-Sufiyya, Mawlayi ed. (1983) 1:159.
5. Shaykh al-`Arusi said in his marginalia titled Nataâij al-Afkar al-Qudsiyya (Bulaq, 1920/1873):
"Religion (al-dîn) is an orchard of which the fence is the Law (al-sharî`a), the inner grove is the Path (al-tarîqa), and the fruit is the Reality (al-haqîqa)."The way of the Sufis consists in ten items:
Whoever has no Law has no Religion; whoever has no Path has no Law; and whoever has no Reality has no Path.
(1) The reality of tasawwuf which is defined by truthful self-orientation (sidq al-tawajjuh) to Allah Most High.
(2) The pivot of truthful tawajjuh is to single out the heart and the body for [obedience of] Allah Alone.
(3) tasawwuf in relation to Dîn is like the soul in relation to the body.
(4) The Sufi examines the factors of perfection and deficiency.
(5) The Jurist examines whatever discharges liability (mâ yusqitu al-haraj) while the scholar of juridical/ doctrinal Principles (al-usûlî) examines whatever makes one's faith valid and firmly established. Therefore the Sufi's perspective is more specific than both of theirs, consequently their criticism of him is valid, while his criticism of either of them is invalid.
Hence 'the Sufi among Jurists is better than the Jurist among Sufis.'
(6) To display the nobility of tasawwuf, its evidence being both by demonstration and by textual precedent (burhânan wa nassan).
(7) fiqh [jurisprudence] is the precondition for the validity of tasawwuf and that is why it has precedence over it.
(8) Terminology and its specific applicability to each discipline exclusively of others.
(9) The keys of spiritual opening concerning which there are four rulings:
first principles; truthful aspiration towards attainment; longing for spiritual realities; and quitting the guideline of what is transmitted (al-manqûl) once one obtains self-realization (al-tahqîq).
(10) It is a wonderful and strange path built on the permanent following of what is better and best: in doctrines it consists in following the Salaf; in rulings, fiqh; in meritorious deeds (al-fadaâil), the scholars of hadith; and in high manners (al-âdâb), all that is conducive to the wholeness of hearts."
6. Some definitions of sufism: tasawwuf:
Purification of the self from all that is other than the remembrance and obedience of Allah; the realization of ihsân (excellence); zuhd (asceticism) combined with ma`rifa (knowledge of Allah); the attribute of the Sufi. Ceasing objection (al-Su`luki); Abandoning the world and its people (Ibn Sam`un).
tasawwuf is neither knowledge nor deeds but an attribute with which the essence of the Sufi adorns itself, possessing knowledge and deeds, and consisting in the balance in which these two are weighed. (Ibn Khafif)
Some definitions of the Sufi:
Sûfî, pl. Sûfiyya: One who follows the path of tasawwuf, He who gazes at the Real in proportion to the state in which He maintains him (Bundar). They wore wool (sûf):
“I found the redress of my heart between Makka and Madina with a group of strangers - people of wool and cloaks - (ashâb sûf wa `abâ).” Sufyan al-Thawri as cited from Khalaf ibn Tamim by al-Dhahabi, Siyar A`lam al-Nubala' (Dar al-Fikr ed. 7:203).
7. As for the following misguided citations:
[refering to the deragatory: "The Other Side of Sufism" at: www.qss.org; but see instead "From the Fatawa of Shaykh al-Azhar `Abd al-Halim Mahmud," (the chief religious authority in Egypt) : On Sufism at: www.uga.edu/islam; OKN]
A parting note. Ibn `Abd al-Hadi narrates in bad' al-`Ilqa bi-Labs al-Khirqa that Ibn Taymiyya boasted of having received the Qadiri Sufi Tariqa from Ibn Qudama. For his part al-Dhahabi in his Siyar twice states he received the Suhrawardi Tariqa from his beloved Egyptian Sufi teacher Ahmad al-Abarquhi. Siyar (Fikr ed. 17:118-119 #6084, 16:302 #5655). He boasts the same in his Mu`jam al-Shuyukh.
And the Hafiz who surpassed both of them, Ibn Hajar al- `Asqalani, was a Shadhili Sufi - as were his students al-Sakhawi and al-Suyuti.
In Sunni Islam it is unthinkable that a learned person not be a Sufi.
 [Sources for Imam al-Shafi`i's saying:]
 [This saying by Imam Malik] does not appear in the early reports but in late works such as:
- `Ali al-Qari, Sharh `Ayn al-`Ilm wa-Zayn al-Hilm (Cairo: Maktabat al-Thaqafa al-Diniyya, 1989) 1:33;
- Ahmad Zarruq, Qawa`id al-Tasawwuf (Cairo, 1310);
- `Ali al-`Adawi, Hashiyat al-`Adawi `ala Sharh Abi al-Hasan li-Risalat
Ibn Abi Zayd al-Musammat Kifayat al-
Talib al-Rabbani li-Risalat Ibn Abi Zayd al-Qayrawani fi Madhhab Malik
(Beirut?: Dar Ihya' al-Kutub al-`Arabiyah,
 [Sources for the saying of] Sufyan al-Thawri: "the best of people is the Sufi who is versed
Al-Harawi al-Ansari (d. 481) narrated it in the chapter on Sufyan in his
Biographical Layers of the Sufi Masters.
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 [Sources for the saying of] Sufyan al-Thawri: "the best of people is the Sufi who is versed in fiqh."
Al-Harawi al-Ansari (d. 481) narrated it in the chapter on Sufyan in his Biographical Layers of the Sufi Masters.