That is not completely true. Depending on the hardware, the "at the time of capture" stabilisation might be doing exactly the same as the post-processing.
On the other hand, the post-processing stabilisation has access to "future frames". So for example it can recognise that you started panning to the right, and are not shaking right at a certain point in time.
But for at-the-time-of-capture stabilisation, it's easy to move the "area to grab" around on the sensor. Thus you don't have to drop a bunch of pixels on the sides possibly followed by scaling the whole image to make up for it.
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