I finally found what I have been looking for.
All over Etsy people had birthstone charms on custom necklaces that were flat swarovski crystals set in a ring of silver, or gold. Most called them crystal charms or birthstone drops or something of that nature, but if you search these terms, you get little to nothing in supplies, or in a google search. I looked in all of the swarovski pendant and bead sections on every jewelry supply website I could find, nothing.
Finally today I discovered they are called Swarovski Channels, and are in the components section of supply websites, not pendants or beads. Also I learned you can get them with two rings. Obviously I have seen jewelry made with these, but didn't know it was something you could just buy. You will be seeing some projects with these in the future. Here they are on my favorite supply website Fusionbeads. And here is a little etsy round up of my favorite ways to use them:
I love an offcentered necklace like this
you can use the two-ringed ones mixed with other beads and chains to make all sorts of necklaces
and you can make simple earrings
or add them to other findings to make something unique