The name brand in the US is Kraft Singles, but at least here that type of orange cheese is just referred to as American regardless of brand

I've never heard of Chester cheese. There's Cheshire cheese, but that's quite crumbly and wouldn't hold up to being packaged like this. You might also be thinking of cheddar. A genuine cheddar would be too brittle, but in modern marketing, cheddar is often shorthand for any homogenous, yellow cheese. So this stuff might be described as cheddar on the packet.

I think this stuff is more of a cheese-flavoured sauce, that they inject into the bags and leave to set. It's more an invention of the convenience food industry, than any culinary tradition.

The British don't know anything about food either.