A captive ring is one that is cut away from the middle of a blank and spins freely but can not fall off either end due to there being a section of a larger diameter on either side of the ring. There is a special tool made for turning them however videos by Alan Lacer and Bonnie Klein (among others) show how to make them with standard turning tools.
Personally, I wouldn't think much of a captive ring on a bottle stopper as it might get in the way of the functionality of the stopper. I like your designs. They are balanced, interesting, and provide plenty of surface to grab without sticking a point in the middle of your palm.
Well done!