Hi there Embrophy and welcome!
Here's what I can tell you about optical image stabilization (IS).
Some telephoto lenses, zoom lenses and digital cameras and digital video cameras come with an optical element that's attached to gyro sensors/gyroscope. This arrangement helps counteract the movement resulting from less than steady hands. It allows for handheld photography at slower than usual shutter speeds given the focal length and does not negatively impact resolution. (Note: You need to be sure to turn off IS if you are using a tripod otherwise the floating IS system can actually blur your image.)
Now, vari-angle prism systems are one type of optical image stabilization method and incorporate two glass elements. The optical system moves in the opposite direction from the moving camera.
Tip-tilt sytems use a tilted single lens element which is, therefore, lighter in overall weight. This is used in high-end binoculars and telescopes. I've read that this system uses less battery power but to what degree, I don't know.
Sorry I don't know more of the technical details. Perhaps someone else does and can add to this.

Cheers,
Deb