Thanks to both of you. With the new pictures, I see it is an actual pearl, not a mabe. If it is keshi, it is not natural and it most likely came from China.
As for the baroque, it looks like a baroque freshwater, natural or cultured. That is the trouble with freshwaters, it is hard to tell the old naturals from the new cultured ones.
The setting looks modern, with a look back to art nouveau shapes. The Royal Hawaian was selling mostly, if not all, newly made jewelry, top of the line, often made by local artisans -and sophisticated ones at that. Artisans who had access to the latest and best materials could have gotten new Chinese cultured baroques a lot easir than century old natural freshwaters from America. Unless you can show the ring is old, I would go with Chinese.
Now if you had gotten the ring in an area of the US where they are still selling natural freshwater pearls, you would know it, because they advertise it loudly and feel bound to educate you about these mussle-y creations. If they had been kicking around your grandmothers' jewelry box or passed down by auntie, they would more likely be old, wild, Freshwaters.
In any case they are both wonderful pieces with beautiful pearls.