Jinni Bottles

Jinni bottles in general are simply containers for Jinni. It doesn't have to be a bottle either. They can be lamps, rings, necklaces, cupboards, mirrors, or even crystals. If you happen to have a Jinni, you can wish their vessel into any shape you want. However, bare in mind, they are designed to be lost or stolen. So, you could wish for a pet tiger, and by the time the wish started to go terribly wrong, the ring could have at some point, slipped off your finger and then you'd be stuck with an angry tiger in the living room and a Jinni who is long gone. You're dead.

The Jinni bottle mentioned in the book is special, though. The Fates cursed the receptacle to not just house Damien, but also to be a portal to a prison cell in Tartarus. No other Jinni bottle/ring/lamp is like that. Just his.