I believe the confusion is arising because our story differs from that of the OT:
".........satan's original name in the Noble Quran was Iblis:
Let us look at the following Noble Verses from the Noble Quran:
Adam was first created on Earth: "Behold, thy Lord said to the Angels: 'I will create a vicegerent on earth.'...(The Noble Quran, 2:34)"
Iblis became Satan: "Behold! We said to the Angels, 'Bow down to Adam': they bowed down except Iblis. He was One of the Jinns, and he broke the Command of his Lord....(The Noble Quran, 18:50)"
"It is We Who Created you and gave you shape; then We bade the Angels bow down to Adam, and they bowed down; not so Iblis; he refused to be of those who bow down. (Allah) said: 'What prevented thee from bowing down when I commanded thee? He said: 'I am better than he: Thou didst create me from fire, and him from clay. (Allah) said: 'Get thee down from this: it is not for thee to be arrogant here: get out, for thou art of the meanest (of creatures). He said: 'Give me respite till the day they are raised up. (Allah) said: 'Be thou amongst those who have respite.' He said: 'Because thou hast thrown me out of the Way, lo! I will lie in wait for them on thy Straight Way: Then will I assault them from before them and behind them, from their right and their left: Nor wilt Thou find, in most of them, gratitude (of Thy mercies).' (Allah) said: 'Get out from this, disgraced and expelled. If any of them follow thee - Hell will I fill with you all. (The Noble Quran, 11-18)"
Iblis was a Jinn who was raised and lived with the Angels. He is a powerful Jinn, and Allah Almighty loved him so much that He treated him like an Angel, until Iblis broke Allah Almighty's Commands and turned into Satan and was expelled with disgrace from the Group of the Angels and from Paradise."
Hope that clarifies the difference.....