Both terms are often used for Jinn in general. A Jinn is simply a free unlamped or unbottled Genie. However in the real world of the supernatural we use the term Djinn for especially powerful Jinn. It’s somewhat analogous to the terms Archdemon, and Demon, or Archangel, and Angel. The Arch’s being the the more powerful paranormal beings. The Master Djinn is known as Iblis, or Shaytan. Not to be mistaken with Satan, aka the Devil, who is the Lord Archdemon of all Demons, and Emperor Of Hell. The origins, and stories of demons, and jinn have been confused over the ages since both beings can seem similar to humans who have a limited perception of the true nature of reality. Little is known about Iblis other than the fact that he loathes humankind, Demons, Angels, and all Gods. His dream is to cleanse all the Universe of all beings so he can reign supreme with his Jinn brothers.
The upper echelon Djinn believe that they can combine all Jinn into one super being whose intellectual powers would match that of the Omniverse God who presides over us all. Their goal is to overwhelm his mind, aka the Omniverse itself, and eradicate his core consciousness thereby taking command of the pure thought matrix of our reality. From that point it would be a matter of a mere thought to blink us all out of existence. Once that goal is achieved they would disband, and spread forth across the Omniverse to enjoy their spoils leaving Iblis, and a small group of trusted Djinn as a core unified consciousness that would be the new God of everything. Let us hope this horrific plan is never brought to fruition!