Right okay, djinni must be analyses from a mythological perspective and a literary perspective.
In the mythological origin, djinni are spirits from pagan Arabia that made its way into Islam (one of the major deviations from Judeo-Christianity) and are creatures made of "smokeless fire". They are presumably made around the same time angels are and before humans existed (Adam). In Islamic belief, God made angels, djinni and man to worship Him.
Djinni are said to have far different views of morality from humanity's, and a common saying of them is that "the worst of man is better than the best of djinn". Which goes to show their morality operates on a far different plane from ours. Djinni, like humans, are able to choose their own faiths because they have free will, which technically means djinni can be of different religions (just like humans). They are also said to be able to move at great distances. Satan in Islam wasn't an angel, but in fact a djinn. Djinn may also translate to demons but the Quran makes reference that djinni and djinni who backed Satan are two differemt groups.
Basically djinni are Daedra from Elder Scrolls.
The idea that of djinni granting wishes basically came from Aladdin, who himself was a character from a story in 1001 Nights, a piece of literature and a famous one at that. And while interesting in itself should not mean that all djinni grant wishes.