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...

Perhaps unsurprisingly, in New England jam seems more popular than jelly. The FDA regulates the labels...jelly is made from fruit juice, while jam is made from fruit chunks. The only jelly I routinely see is concord grape jelly. Jams are usually apricot, raspberry, or strawberry.

Given the number of small batch jams available at various farmers markets, my guess would be that for smaller farms, making jam is more practical than jelly.

Unless it's relevant to the conversation ("grab some strawberry jam when you're at the store, not the strawberry jelly"), Americans are also likely to use "jelly" as the catch all for the various "preserves meant for spreading". I guess that's kind of alluded to by my suggestion to put any of them on a peanut butter and "jelly" sandwich.

Jam is more popular than jelly, in my experience, but (as OkayPhysicist said) many people use the word "jelly" incorrectly to mean any kind of fruit spread.