OIS (optical image stabilisation) physically moves a lens element, or on some cameras the sensor, to counter small hand movements while each frame is exposed, so it reduces blur without losing any of the picture. EIS (electronic image stabilisation) records a slightly larger area than the finished video and shifts the frame around inside it from one frame to the next, so it can smooth bigger movements like walking, at the cost of some field of view. Most phones use both at once.
Software stabilisation is a third kind: it works on a clip after it has been recorded, by measuring the movement from the picture itself. It is what you need when the camera’s own stabilisation was off, wasn’t strong enough, or the camera had none. The stabiliser at the top of this page is that kind, and runs in your browser.