When it comes to image stabilization there are two major stabilization types — electronic and optical. But how come electronic image stabilization looks so good on my GoPro but not on my "real" camera?
There are a lot of reasons for this, and this video from DPReview does a fantastic job explaining it. It has to do with a lot of variables, like shutter speed, motion blur, and sensor size. I don't want to spoil the entire video but you may be wondering what the difference between electronic and optical stabilization is anyway?
Basically, Optical Image Stabilization, or OIS, is when physical parts of your camera lens move independently of your camera in order to counteract small amounts of motion, whereas electronic image stabilization does this through software: zooming the footage in and aligning individual frames together in order to try and recreate what OIS does in post production though this isn't without its drawbacks which the video above does a better job of explaining than I could.
EIS can be done either in camera, where it can work in conjunction with accelerometers, or it an be done in post, where you have a bit more control. One thing that DPReview didn't have a chance to touch on in this short video is IBIS, In Body Image Stabilization, which is similar to OIS in that it physically moves something to counteract camera shake but, unlike OIS, is built into the camera but uses the sensor instead of lens elements making essentially every lens you use on that camera stabilized.