Different Djinn have different types of powers and differing limits on their supernatural ability.
Water Djinn: Along with their Djinn inherited traits some Water Djinn seem to possess the ability to alter their appearances [with the exception of their dead eyes]. Alice is an example of a Water Djinn with this capability.
Life Djinn (Vampires): Life Djinn have are capable of returning to life after succumbing to a mortal wound. How this is accomplished is not yet stated.
Life Djinn are also the only Djinn capable of hiding their dead eyes using their Djinn Arts. This ability is called a mask by most and it is what Life Djinns show the world when they are calm and nourished.
"Vampires have the most comparable-to-alive flesh. Other djinn have a composite of organic and inorganic flesh -- the exact ratios vary based on the type of Djinn and how far said Djinn has "advanced" into becoming an Efreet. Sedja, for instance, is completely inorganic at this point." a quote from Jigsaw
Blood Djinn: It should be noted that blood Djinn are not Vampires. A blood Djinn's abilities center around the master of blood itself and not life as a vampires does.
Silk Djinn: "Sedja is a Silk efreet, if that gives you any clues. It's not that more "traditional" elemental efreet don't exist, but it's a lot like picking a major in grad school -- you dictate your element a lot more than your element dictates you. In Sedja's case, her focus on luxurious fabrics and jewelry metals made a focus on Silk (soft as a woven fiber, hard as steel in a condensed form) an excellent element. "
Fire Djinn : cypress was haunted by dreams of a fire Djinn which destroyed her home and attacked her family when she was very young. one might infer that Fire Djinn have mastery over fire heat and light produced by flame. in my opinion it would make them the human torches of the djinn world. though i would not expect them to flay around on fire announcing there presence to the world.