There are several things going on here, and I'll admit I'm only an amateur scholar on such. When Westerners use the word "demon", it could be referring to one of at least two sorts of figures from the collected Middle-Eastern cultures.
In the history of Christianity, there was something called (and someone may correct me if I'm confusing things), "The Manichean Heresy", which said, basically, that Satan/Evil was just as big as God/Good and they struggled back and forth. If this rings a bell for folks, it's because people like Aquinas were influenced, if not convinced, but enough that it became part of "some" teachings.
The Islamic world has no such confusion. While the 10 Commandments say "Thou shalt have no other God before me", the 1st of the 5 Pillars of Islam is to state "There is NO god but God..." So- no contest there, at least not anything like the Good/Evil struggle that rages in the corners of the Christian mythos. There may be evil critters, but not on the same scale as Satan & Co.
Jinn? Folk tales. SAT Statement: "Djinn are to the Arabian Nights as Fae/Ogres are to the Brothers Grimm." A strong cultural theme, but not a "religious" one, so "Djinn as demons" does not translate well- more like "Djinn as magical ogres", or whatever.
The "shatans" mentioned above are, in fact, where we get our word "Satan"- when Islamics denounce the United States as "The Great Shatan", that's what they're referring to. More like an "evil tempter", as I understand it, but hardly a cosmic threat- merely a dire mortal one.
As far as other "fae"- not so much per se, not as we know them, but there are endless magical and mystical folk in literature - fakirs and such that have no explanation beyond "full o' mystery n' stuff". And there are some "gnomes", for lack of a better word, that go waaaaay back into ancient religions of the area (see Enkidu et al) - but again, those are largely going to be "officially" surpressed by Islam, but still found in episodes of "Folktales of the naive and ignorant."
Go to the library and find 1001 Arabian Nights- the unabridged version- pick up a volume (one of the 15 or so) and skim through some of the critters that show up. Then think about everything that shows up in the spectrum of our literature, and use your imagination.
