Correction of lens aberrations in-camera

I'm slightly confused about what is actually done by Olympus and Panasonic in this regard. The pertinent camera and lens reviews don't seem to be completely consistent.

Far as I can tell, if you have a Panasonic m43, and a Panasonic lens, then spherical and chromatic are corrected on-the-fly. But is this the case for Olympus camera-and-lens? What happens if you have a lens from one and body from the other?

Thanks for insights.

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Tim