How about yogurt? In the US, it’s often a sweetened snack, especially for children. But in India, for instance, when making raita , spices and cucumber are added.
Carrots - can be cooked with meat and potatoes in a stew, or served cold in salads, but there is also carrot cake and carrot jam.
Japanese Mochi is often filled with a sweetened red bean paste as well. Very sweet and tasty, but most Americans are unaccustomed to beans being a dessert.
Never heard of a navy bean pie either. Would love to try some one day!
I’ve had lima bean pie. It’s like sweet potato pie, but better.
I had to look up bean pie - that looks delicious. I’ve had candy and sweet baked goods made from bean paste, it is OK.
Are winter squash (pumpkin mainly) and sweet potatoes used in sweet pies or desserts anywhere other than the US?
Growing up in Australia both pumpkin and sweet potato were mainly had roasted with spuds alongside a beef or pork roast. Pumpkin soup was common too.
The only ‘sweet’ thing I can remember pumpkin in was pumpkin scones served with whipped cream and jam.
Jelly can also refer to a substance similar to jam, but with all pips, skin and whatnot strained out in the UK as well. It may not be the commonest use of the word here, but as I’ve just been reading the jelly making section of my 1970 terribly English gardening and home preserving book, I feel I should point it out.
And at least we don’t stick salads in our gelatine desserts.
Mint jelly? Red currant jelly?
In the UK the distinction is the same: jelly is clear, jam has bits. There is also the gelatin pudding called jelly, it has some similarities but is a different thing.
I just learned that this means that Americans really do have jelly on their sandwiches, and aren’t confused about the proper words for things as they usually are. Maybe they just don’t have a lot of jam? The plot thickens, as ever. There will shortly be those saying that all this is only true for certain parts of the country… 
And a sidebar to this sidebar: I can never understand this strange idea that peanut butter and jam would be foreign to the English. My mother grew up with peanut butter and jam sandwiches and she is in her sixties. Some Dopers must be old, like… from before the railways or something.
ETA: high five Filbert! 
That’s the stuff I was talking about!
Another one from a branch of the culture. In a little hole-in-the-wall shop in San Francisco’s Chinatown, I once got what I thought was a jelly doughnut. Inside the sweet bread was sweet jelly filling. Inside the jelly, I bit into . . . something cold and moist and slippery. I nearly gagged, before I realized that it was simply a hard-boiled egg. Once I got used to the idea of an egg being sweet, it was pretty good.
Plenty of jam in the US. Smuckers is probably the most well-known brand.
How would a Biscuit fit into the discussion?
The word seems to mean something completely different in the USA to in the UK, Australia etc.
In Aus, a biscuit could be either sweet or savoury. Both a cookie and a cracker are a biscuit.
I had a delicious pinto bean cake one time, it was like a spice cake.
I just ran across an ad for an avocado milkshake at a local Vietnamese restaurant.
Huh. But that’s not what you put on the peanut butter then? It just doesn’t seem to be talked about much. Whenever I hear anyone referring to jelly/jam in the US it’s “jelly” (obviously, I rarely know what is actually on the toast). In the UK you’re more likely to hear jam, and it is jam.
In short, my question is: do people sometimes call jam jelly, or do you have more jelly than jam, or is it one of those “it’s different all over”-things?
I have to admit that I’m always a bit creeped out when I find a preserved egg yolk inside a sweet Chinese mooncake.
But a scone is never a biscuit in Aus, yet that’s what the US biscuits most closely resemble.
I don’t know what everyone else calls jelly and jam; but peanut butter and jelly sandwiches are always called peanut butter and jelly sandwiches (or 'PBJ’s) whether they are made with actual jelly or jam.
I don’t think people use jam and jelly interchangeable, as they are different. And Smuckers actually sells preserves and “fruit spreads” in addition to jams and jellies. (I used to put Smuckers strawberry jelly on my buttered toast but not strawberry jam.)
We have the same meanings for jam and jelly. You spread both of them on bread. The difference is the consistency; this is jam and this is jelly.
But we don’t use jelly for the second meaning you do. You would also call this jelly but we call it jello.
Unless it’s made out of cranberries, in which case we call it jelly even if it’s actually jello or jam.
eta: I see other people have already addressed these points. But my post has pictures.
Biscuits are almost never sweet in America. (Other than the way our bread products are generally sweet.)
A biscuit is something like this and you might use it to make a small sandwich or serve it with a meaty gravy.
The other meaning of a biscuit is a small treat you’d give a dog.
In Mexico it’s generally savory, but many people drench it in chili sauce (a kind of spicy ketchup, in this case)…which makes going to the cinema a very soggy experience.