Queena, there is camera stabilization, per the video link you provided and image stabilization. Camera Stabilization is mainly used by videographers/cinematographers when shooting from moving/unstable platforms. When employed it will smooth out the video eliminating minor bumps and movements of the moving/unstable shooting platform (car, helicopter, person, et al). These are large, expensive, external affairs.
There is Image Stabilization (IS), which sort of isolates the image from the camera. IS is used for stills and minimises blur due to low shutter speeds and handheld camera shake. IS can be found in the camera (In Body Image Stabilization - IBIS) on in the lens (Image Stabilization - IS).
I do not know how you plan to shoot the wedding ... video or stills or both ... from a moving platform or at low shutter speeds ... so it is difficult to answer a specific question. Reportedly the A7S is remarkable in low light, delivering high image quality at high ISO's. Which makes me assume that you are more concerned with shooting from a moving/unstable platform than shooting at low shutter speeds ... so ... I would think you are seeking camera stabilization for video. I would read a ton of reviews and start whittling down my choices. Then as Unpopular stated rent a few camera stabilization choices then decide based upon usage.
I think most here shoot stills and not a lot of video and are not very familiar with camera stabilization (as opposed to image stabilization).
Remember that generally, both systems only work on the camera end not the subject end.
1) If you're using CS/IS/IBIS and shooting a person running in front of a building with a slow shutter speed, the runner will be blurred but the non-moving building will be sharp.
2) If the same shot was taken, (low shutter speed), without CS/IS/IBIS, both the runner and the building will be blurred (the runner will display more blur than with CS/IS/IBIS, but it will still be blurred).
3) If your subject is stationary and shot with a low shutter speed with CS/IS/IBIS, then both subject and stationary background will be sharp. If your subject is stationary and shot at a low shutter speed without CS/IS/IBIS then both subject and stationary background will be blurry.
A simple tripod mounted on a non-moving platform, will outperform a handheld camera using CS/IS/IBIS.