Cross-referencing between rosamicula, Merrianm-Webster, the OED, and Amazon.co.uk, it really does look like "cutting board" is generally what is used in the US and "chopping board" is what is used in England. Fascinating. I have failed to notice this, however many I have bought.
There was widespread ambiguity in some of these sources, but the lack of entry for "chopping board" in Merriam-Webster clinched it for me.
Canadians? Which would you ask for, if you went shopping for a flat chunk of wood on which to take apart vegetables or meat by means of a knife?