How does one account for the fact that people are getting great indoor shots [prom pix] with little P&S cameras? It blows me away...a friend of mine had one of those little square cameras and was snapping away at a night-time sports banquet--she had to send them to me because my Fuji pix [with flash] were all blurry--of the same shot!
Buy your friend's camera. ;-)
Look, it's a matter of aperture, ISO speed and light (as I mentioned in my first post).
Most smaller cameras are not going to have apertures wider than f/2.8 on their wide end, and most will lose a lot of light as you zoom in more.
Most small cameras won't have usable ISO speeds above about ISO 400 (and most will have quite a bit of noise/grain at that ISO speed). At smaller print/viewing sizes, you may not notice it.
Light in a typical indoor environment runs at an EV (Exposure Value which is a way light is measured) of around 6. Some environments may have better light, and some may have worse light.
At f/2.8, ISO 400 with light at an EV of 6 (typical well lit home interior), you can expect shutter speeds of about 1/30 second. That's going to be at least 4 times as fast as you're getting with your Fuji model (it's much worse than most cameras).
But, that's still not fast enough to stop all motion blur if you're shooting a moving subject and not using a flash.
If you keep viewing and print sizes small, then blur won't be as obvious.
For a rapidly moving subject (as in basketball in most indoor gyms), you may need shutter speeds 5 or 10 times as fast you'd get with most smaller models to stop all motion blur. What you can live with is subjective.