The Derbyshire grit millstone (or Peakstone as it is also known) is cut from the ground in one piece. Here we see a couple of piles of abandoned stones in the area around Hathersage. It appears that one day there was a millstone industry and the next day there wasn't. It's as if everyone just walked off site leaving surplus stock behind them piled at the side of the track ready to be taken away. The Peak District National Park adopted the millstone as its emblem. Peakstones, particularly the smaller ones, also found widespread use as grinding stones for the sharpening of cutting tools from the Sheffield steel foundries. (One day I hope to get back here when the sun is shining.)
For a bit more on Derbyshire Grit Stones, have a look at this page on the Peakscan site.
The French burrstone on the other hand was always assembled from a number of smaller pieces of stone. Here we see a couple that have been reused as wall decorations.