What do you mean by scanning size, edition size and release size?
Imagine that your final image is 4000pix wide with 8bits/channel. You may make the edition of a 6000pix wide image with 16/bits channel that you reduce to 4000 / 8 bits when edition finished. In the same way if your edition is made with 6000 pix wide you may scan the image to get 8000pix wide.
So you scan with more dpi than "necessary" to extract the last bit of image quality (always 16 bits per channel), then you sharpen and reduce the image size while no nothing is lost to get an smaller image that's faster to edit, but still your edition is made in a resolution that's larger than your intended final image.
Finally you reduce the image size again to (perhaps) issue an image pixel for each pixel (ppi concept) the printer prints. A printer may use several dots to make pixel, hence the ppi vs dpi concept.
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Let me extend my answer...
When printing you have two choices, first is crafting a printable image that has a pixel for each pixel the printer will print, in that way you have absolute control, but this requires you craft an optimal image, also making a final sharpening at "pixel level".
Another choice is sending to printer and excedingly large image, you may send an image with 30% more pixels in a row than those that the printer will print, given ppi and print size, in that case (not printing 100%, but 70% to fit your print size) the printer driver makes the necessary size conversion. Amazingly this may yield very good result because the printer drivers today are quite wise and they know how to make a good optimization of the reduced image, even it can be better than a manually made size conversion to match the print size.
Me, I prefer crafting an image that will print 100% (one to one pixel), to have total control, or at least to preview well the final result, but I know wise people that prefer delegating that job to the printer drivers.
In the same way an image that has to be displayed in an screen may be downsized to the screen size (from edited size), reduced to 8bits/channel, and (perhaps) jpg compressed to the point we don't have a loss.
Anyway a powerful edition benefits from Photoshop layers, not to be intrussive in the image but to be able balance well our tonality management. Then sometimes the edited image may contain layers, so the PSD format file containing layers may be very big, we may want to conserve that PSD file if later we want to make modification in one of the layers in a non destructive way: this is very important if editing for a client so we can finely suit his taste, but this is also a good practice for important personal images, for this reason we should reduce the scanned size to a smaller edition size, because when we add layers then our file size my multiply the base size of the image.