There are many similarities to genies from Arabic Mythology and the yokai from Japanese folklore. However, there are differences as well.
Our term genie is the English spelling and pronunciation of jinni (djinni in Latin). Jinni is singular, while jinn is plural. The jinn were a pagan concept that existed in the Pre-Muhammadan age and was incorporated into Islamic theology as one of the three types of spirits. The spirits include the jinn, angels, and demons. The jinn differed from the other two types of spirits because they could be good or evil. Angels, always good, Demons, always evil.
In Pre-Islamic traditions, jinn inhabited desolate places, like the deserts, dark caves, unclean places, etc. Some tribes believed they delighted in tormenting humans and one must placate them or have some power, such as a talisman, to protect themselves when in those places. We can compare the jinn to the “fallen angels” from Christianity, who are reputed to dwell here on Earth as well.
One of the common beliefs about jinn was that they were created by Allah (God) before he created Adam. They were created from “smokeless fire,” think purely spirit. Many tales gave them certain powers, usually always magical (like the Genie of the Ring or Genie of the Lamp from A Thousand and One Nights). By the way, not really sure where the concept of Three Wishes came from, both genies in Aladdin’s tale could grant as many wishes as their “master” wanted!
Jinn could assume the form of animals, or practically anything they wished.
Now, the yokai. They are a class of supernatural beings, spirits and demons. The word yokai is comes from kanji meaning, "bewitching; attractive; calamity" and "specter; apparition; mystery; suspicious." Yokai can be evil (such as the one seen in the movie 47 Ronin), or simply mischievous (similar to brownies from European folklore). Some tales describe yokai as bringing good fortune to people that interact well with them.
Yokai often possess animal features (like the turtle-like kappa or the bird-winged tengu). Others appear as mostly human. Some yokai resemble inanimate objects like hills, mountains, rocks, shrines, etc. Still, others have no discernible shape at all, appearing as mist, fog, liquid, etc.
Yokai usually possess supernatural abilities, shapeshifting is the most common (again the yokai in 47 Ronin could shapeshift from human to fox to dragon).
Now, to explain why they are not the same. Japan was, for most of its pre-American years, isolated from the rest of the world. They had little or no interactions with other cultures, especially one as far away as Arabia. Therefore, the belief in jinn was not an influence on the Japanese. Their belief in yokai came from their belief in animism (everything had a spirit). So, both “types” of genies emerged at the same time.
Hope this helped.