The sentient incarnations of the primal elements of creation, the jinn are masters of the realm of Chaos. Nobody quite knows how or when the first jinn were created. It may have been the will of some higher power, it may have been that the elemental realms evolved entities complex enough to attract a soul, or it may have been the elemental domains mimicking the mortal realm and creating their own version of sentient creatures.
Generally, jinn are free-roaming, free-willed beings who are able to manifest wherever they please. However, just like any other supernatural being, a jinn can be bound. Indeed, because of their wishcrafting powers, jinn are perhaps the most common race for mortals to bind into service; the power of wishes is far more beneficial than a fey's glamours or a horror's terrors. Thus the rather common tale of the genie in the ring or lamp, or the wish-granting gem.
An unbound jinn can grant whatever wishes they so desire. Generally, a jinn would only do so if they greatly valued and respected the one whose wish they were granting--a close friend or a lover--or in exchange for a great favour at a later date. However, when bound, it all depends on the binding. A weak binding may only call a jinn's attention and force them to listen to the wish, a moderate binding may prevent a jinn from leaving until the wish is granted, and a strong binding strips away the jinn's free will, dominating them and forcing them to perform the desired actions. These bindings can either be one-shot calling rituals as you describe, or powerful seals that can lock a jinn into a vessel. These seals typically only hold for three wishes before their runic magic is expended and the jinn is free to leave, though there are some that last for a single wish, or seven.
The jinn roam the elemental domains of Chaos and the mortal realm freely, and some even take jaunts to Faerie or Shadow. They are free to travel as any other besouled being. Of course, travelling to the mortal realm does increase the risk of them being bound, but on the other hand, the mortal realm is a much more interesting place than the roiling chaos of their home realm.There are those who prefer the elemental domains, of course, as well as many who serve in the courts of the various jinni nations, but they're a minority among the jinn population.
Jinn have a natural inclination towards their own element, and talent in the powers thereof, but like any besouled being, they can choose their own path in life. However, jinn of differing elements have been known to work together to create truly grand creations, or grant magnificent wishes.
There are several kingdoms of the jinn, each affiliated with a particular element, and that would-be rulers often proclaim that they have discovered a particular region of the elemental realm represents a new, unique element on its own, such as the numerous jinn who have attempted for forge kingdoms of ice, or shadow, or thunder... or that one madman who created a kingdom of ooze. The most successful of these have been the bestial nasnas, who have ensured the kingdom of wood is at least begrudgingly accepted as at least a partially official elemental realm.
Now, each of the various kingdoms is headed by a powerful, ancient jinn, most notable being the efrit's Emperor of All Flame and the Bejewelled King of the gnomes. Beneath them are various nobles, who obtain their positions either through service to the crown, personal power, or family lineage if one of their ancestors was granted a hereditary position. The exact details would likely vary from kingdom to kingdom, and from ruler to ruler.
These elite jinn live a life of luxury, for they get to enjoy the full benefits of a race able to wish almost anything into existence: grand palaces, the finest foods and works of arts, and the like. Indeed, because of this decadent reality, I was thinking that noble jinn especially value creativity, since creativity isn't something that can be wished into existence. Therefor, a noble jinn may pay exorbitant amounts of money during a trip to Earth to obtain a great piece of art, or a unique car, or the finest wine.
The lower classes don't quite get to enjoy the same standard of luxury as their noble kin. Their lives are likely of a higher standard than almost any other supernatural, though, with only the dragons and a few noble fey or highborn horrors holding a candle to the experiences of even the common jinn enjoys. However, their power and influence can expand much further in the mortal realm, and thus many will travel to Earth to try and make their own way. Others will become servants for the noble houses, and serve them in hopes of slowly rising through the ranks and eventually joining the privileged elite one day.
Wishes are a cornerstone of jinn society, and defines who and what they are. No other race can grant a wish like a jinn. This is because of their close ties to the primal forces of creation. Therefor, a jinn can wish almost anything into existence, but creating living things are incredibly difficult, and creating a besouled being is impossible. Likewise, this allows a jinn to emulate other forms of magic with their wishcrafting... which is how a jinn may get someone to fall in love, or grant one great strength, stamina, or charisma. Asking a jinn for unlimited wishes is pretty much impossible, as a jinn physically cannot grant more than maybe a half-dozen wishes a year without stretching themselves too thin and risking their own lives in the process. Why the whole "three wishes" on a seal or binding is common: it guarantees the bound jinn won't die, and thus you won't have the jinn's furious ghost haunting you for eternity (after all, pretty much any besouled being which dies a traumatic death has a chance of coming back as a ghost, and forcing a jinn to wish itself to death is quite traumatic).
One thing to note: wish is more powerful the stronger the wisher desires it to come true. The wishcrafting of the jinn jumps on the power of desire and imagination to transform reality. Therefor, a jinn may sometimes need to rely on another to make a wish for them, just in case the jinn themselves lacks enough passion or imagination to create exactly what they need at that moment.