In the Arabic language, Shaytan is derived from Shatana, which means the far thing. Hence, the Shaytan has a different nature than mankind, and his sinful ways are far away from every type of righteousness.
It was also said that Shaytan is derived from Shata, (literally `burned'), because it was created from fire. Some scholars said that both meanings are correct, although they state that the first meaning is more plausible.
Further, Siybawayh (the renowned Arab linguistic) said, "The Arabs say, `So-and-so has Tashaytan,' when he commits the act of the devils.
If Shaytan was derived from Shata, they would have said, Tashayyata (rather than Tashaytan).''
Hence, Shaytan is derived from the word that means, far away.
This is why they call those who are rebellious (or mischievous) from among the Jinns and mankind a `Shaytan'.
Allah said,
ۚوَكَذَٰلِكَ جَعَلْنَا لِكُلِّ نَبِيٍّ عَدُوًّا شَيَاطِينَ الْإِنسِ وَالْجِنِّ يُوحِي بَعْضُهُمْ إِلَىٰ بَعْضٍ زُخْرُفَ الْقَوْلِ غُرُورًا
(english meaning)
(And so We have appointed for every Prophet enemies Shayatin (devils) among mankind and Jinn, inspiring one another with adorned speech as a delusion (or by way of deception)) (6:112).
In addition, the Musnad by Imam Ahmad records that Abu Dharr said that the Messenger of Allah said,(english meaning)
(O Abu Dharr! Seek refuge with Allah from the devils of mankind and the Jinns.) Abu Dharr said, "I asked him , `Are there human devils' He said, (Yes.)'' Furthermore, it is recorded in Sahih Muslim that Abu Dharr said that the Messenger of Allah said,(english meaning)
(The woman, the donkey and the black dog interrupt the prayer (if they pass in front of those who do not pray behind a Sutrah, i.e. a barrier).)
Abu Dharr said, "I said, `What is the difference between the black dog and the red or yellow dog' He said,(english meaning)
(The black dog is a devil.).''
Also, Ibn Jarir At-Tabari recorded that `Umar bin Al-Khattab once rode a Berthawn (huge camel) which started to proceed arrogantly. `Umar kept striking the animal, but the animal kept walking in an arrogant manner. `Umar dismounted the animal and said, "By Allah! You have carried me on a Shaytan. I did not come down from it until after I had felt something strange in my heart.''
This Hadith has an authentic chain of narrators.
Extracted from English translation of Safee ar-Rahmaan al-Mubaarakfooree's abridgement/re-writing of Tafseer Ibn Katheer called al-Misbaah al-Muneer volume one pages 57-58
Darrussalam edition
slightly modified for transcription purposes:
[some arabic text omitted]
