The US is the strange one, vis-a-vis "Jelly"
Pretty much every other english speaking country calls what we call "Jelly", "Jam."
Here in the US, "Jam" has a special meaning; It's got bits of fruit in it, where Jelly does not. In the UK (and most english speaking countries), both are "Jam".
In the US, we take it even further, and have an ADDITIONAL name for the stuff, if it also has the seeds in it. "Preserves". Again, In the UK and co, "Jam".
I've seen jams called preserves over here in the UK. But in general, you're right.
Also jelly is a dessert.
That is precisely my point! For you, "Jelly" is the stuff you put into a mold, and chill in the refrigerator for a few hours. It's made out gelatin, extracted from boiled bones, mixed with a colorant and a fun fruit flavoring.
For me, that stuff is called "Jello". (It's the major name brand for the product, which gained traction as the name for the desert, even though the desert is FAR older than the jello company. Jello made it easy to make, with the convenient "Add hot water then cool" packets, which transformed it from a thing only very rich people who could afford a dedicated cooking staff ate, into a commodity dessert.) I suppose more properly, it's a "Gelatin dessert". But everyone just calls it Jello. "Jelly" is the stuff you put on toast. For you, that's "jam."
This "Same word, very different meaning" leads to utter disgust when the topic of "Peanut butter and jelly" comes up. Americans are like "Oh yeah, I ate that all the time as a kid" and people in the UK go "What the bloody hell is wrong with those Yanks?"

RE: Arx
In the US it's usually the other way around. Cranky old people will demand actual jellies, instead of jams. (Mostly because they dont like the fruit bits in their false teeth I think.)