Regarding Britain, "conserve" used to mean posh jam, but nowadays it seems to be more of a marketing word - a brand trying to pretend they're posh, similar to how pretentious restaurants use French words for no obvious reason.
"Smooth jam" here in the UK is sometimes labelled as jelly, like this kind of thing:
https://www.ocado.com/products/tiptree-blackberry-jelly/1053...
interestingly, i think there's also a u vs non-u thing here: jam is a u word, preserve is non-u