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Regrinding, especially back in the early 1800's, consisted of 1) a guy who knew (or mostly knew) how to do it 2) a stool 3) a grinding wheel, powered by a pedal. Some grinders had more things -- the...

This might help clarify:

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Two razors, one has had its finish reground, the other hasn't.

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In the closeup, it's obvious.

These razors were almost certainly put on a grinding wheel to clean off rust and remove pitting. It was a thing that was done pretty commonly.

I know these days when we see 'regrind' we think of...