Iblis - this refers to the name of a Jinn who was raised to Jannah (Heaven) on account of his piety. There is a debate about the origin of his name, some scholars believe it comes from the verb balasa meaning to despair as in 30:12, 6:44, 23:77, 30:49 and 43:75. So Iblis refers to the one who despaired or despairs.
We know he is a jinn because, in 18:50, Allah says, '… except for Iblis. He was of the jinn' and Iblis himself says in 7:12, '… You created me from fire…' and the jinn were created from fire as stated in 15:27 and 55:15. Iblis is the Shaitan in the Qur'an. He is given respite to confirm his assumptions (15:39, 34:20) that man is naturally ungrateful and undeserving of the respect Allah gave him.
Shaytān - We have confirmed that Iblīs is indeed the archetypal shaytān in the Qur'an and the foremost of them. But he is not the only one. This is confirmed in numerous instances, 6:121, 7:27, 7:30, 17:27, 19:68, 19:83, 22:82 etc. The word shaytān appears in the plural in all of these verses.
If you read the last Surah of the Qur'an, Surah Nās, 'Say I seek refuge with the sustainer of mankind • … • from the jinn and mankind •' Refuge is sought in the same way one seeks refuge from the shaytān, implicit in it is that the Shayateen (devils) can be from among jinn and men.
An interesting fact to note is the the word for devil, shaytān, is repeated 88 times. The word for angel, malak, is also repeated 88 times as if to emphasise the dichotomy between the two and the battle between good and evil. Malak comes from the root verb malaka which means to acquire/gain possession of. Shaytān comes from the root verb Shaitan meaning to bind/fasten (as with a rope). So even the names really symbolise the tug of force between good and evil.
To conclude:
I hope this helped.
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