Not going to speak for bedir than (would be very interested to hear their thoughts!), but I wanted to comment on this too.
From what I've understood, the Efreet are a variety of Djinni in some Arabic traditions (Ifrit of the Jinn/Efreet from the Djinn), while in others they are separate but related beings (in the same sense that Sylph, Salamander, Ondine, and Gnome are related in Paracelsus's writings). Meanwhile, Marid and Ifrit/Efreet are used somewhat interchangeably, and Dao doesn't exist (but Ghuls/Ghouls do). Sometimes Djinn are demons, sometimes they're angels or deities (esp. if referring to neighbouring cultures' gods & idols), sometimes they're nature spirits, sometimes they're faeries/elves, sometimes they're the in-between between angels and demons… It depends on writer/storyteller/time period/setting.
Still weird to use Genie as inclusive of Djinni, but I gather the idea was to have Genie mean the broader usage that includes Efreet, and Djinni the more specific, air-elemental usage of the term. It's weird, and I wouldn't recommend it to anyone writing their own fantasy setting, but these sorts of nebulousities are not entirely unsurprising.