Aye that. I've been in this faith for other 25 years, long enough to see it go through some strange changes in practice. When I first came into this faith, the American Muslim practice commonly used more than one name for each person, sort of to symbolize growth and development. So, I started off as Brother "Yaya" (something like John), and then "Hajji" and then was ceremonially renamed "Japah", and then Sahaj.
Now of course, since the Islam faith has the same cultural roots as those from which Christianity came, we should definitely expect a lot of parallels. This would be just like the parallels you find between Christianity and the Hebrew Judaism. Muslims accept Jesus (Yeshua) as at least having been a very important and powerful prophet/ healer.
Satan is referred to as "Shaitan" & "Iblis" in Muslim or Islamic faith. Shaitan would sort of like an English adjective that may be used in reference to men and spirits. Iblis would be our term for the evil entity known more commonly as Devil, and is found in our Quran version of the Genesis story.
Now, the primary difference between our view of this entity and that of Christians is that we see Iblis as a "jinn", not as a fallen angel. You see, we see the angels as being servats of God/ Allah, lacking any free will of their own. This is why so many say that man is the greatest creation of Allah. A "jinn" is a spiritual entity made from smokeless fire (an idea we find in your story of Moses, who looked upon a burning bush that was not consumed by the fire) and Iblis came into infamy as a result of pride and jealousy, having refused to bow before Adam when so ordered by Allah.