As a Brit the first thing I imagined was one of those large, thin plastic boards, usually green, with a grid of various measurements and angles printed on them, used for cutting fabric for sewing patterns.
In the US those are usually called "self-healing cutting mats" made of PVC (indeed, a plastic).
In the US, I have some "cutting boards" made from flexible self-healing plastic.
To add confusion: These are for kitchen use.
To add more confusion: They were purchased from Aldi.
Me too - I think 'cutting' implies a level of precision that 'chopping' doesn't. After all, I don't think even Michelin-star restaurants require that finely-sliced carrots!