Bridge cameras tend to trade off reach for low-light capability. Both of your images look like they were taken in indoor enclosures, and the camera maxed out to iso 1600, which was needed given the small aperture and long shutter speed (i.e., you needed more light).
The high ISO setting with the small sensor of the S8200 (1/2.3" format) is the cause of the noise. But it kept you from having camera-shake blur and underexposure.
If your subjects aren't moving, you could possibly lower the ISO and use a lower shutter speed if you stabilize the camera somehow (tripod, monopod). Or you could add light into the scene with a flash. But if you want to handhold a camera without additional equipment, then the only way to get better low light performance is to get a camera with a larger sensor, use a "shorter" lens (i.e., zoom out); or use a "faster" lens (one with a larger maximum aperture). Obviously, this will most likely call for a different (and more expensive) camera.
If you want to stay with a Fuji fixed-lens bridge camera, the Fuji X-S1 might help, as it (unusually) uses a 2/3"-format sensor (4x vs. 5.6x crop factors), but it will cost US$150 more. And it still might not get you the performance you want. An APS-C sized sensor (1.5x crop) and interchangeable lenses is probably the way to go, but would cost thousands of dollars.