"jam," "jelly," and "jello" in AmEng vernacular
Solution 1:
What exactly is the fruit preserve called "jam" in the U.S? [my emphasis]
I'm answering the question from the point of view of language, what these words mean to the speakers who use them. Thus, many speakers might call a fruit spread in a dish jam or jelly based on regional preferences rather than on the actual recipe.
Many foods on the American supermarket shelf are not what their labels say they are, so many Americans could not tell you the difference between jam and jelly, only that they tend to use the one or the other word. For many speakers, these words refer to a sweet spread, gelatinous in texture, that seems to be fruit-based (grape, blackberry, blueberry, strawberry, etc) though it may contain no fruit only fruit-juice, or no real fruit product at all, merely some artificial fruit flavoring and coloring.
Jello is a tradename for a rubbery (artificial) fruit-flavored gelatin.
Here's the federal definition per Consumer Reports in a little blurb about the differences, and that's usually a good indication that many people don't know the difference. spreadable fruit and fruit spread are terms without federal definition.
Solution 2:
You wrote, "In other words, what would Americans commonly call the "confiture" and "gelée" preserves typically found for breakfast in every French hotel?" The answer, taken from your choices, is "'jam' and 'jelly.'"
In America, jam includes the fruit in the mix; it is thicker, richer, and a bit lumpy in texture. It is spread on toasted bread that has been buttered first. It is also wonderful on vanilla ice cream. Jelly is used in the same way, but it is made from strained fruit and has uniform, smooth and "clear" texture, containing no lumps or pieces of the fruit from which it is made. Americans usually prefer one over the other, but many enjoy both. Jelly spreads more easily (as on a peanut butter sandwich), but jam offers more texture and flavor. We also enjoy marmalade, but use it less frequently and sometimes in different ways, for instance, as a complement to meats like pork.
Jello (tm) is a clear, colored gelatin dessert that is also used to make salads when combined with chunks of various canned fruits and/or marshmallows. In the latter case, it is often chilled and formed in a mold to give it a distinctive shape, with a scalloped top and a hole in the center, the same type of pan sometimes used to make a coffee cake or similar baked dessert. Jello comes in a box as a powder, to which one adds water and sugar while heating the mix. Once the liquid is uniform and clear, it is poured into a glass baking dish or pan and then placed in the refrigerator to chill into the firm, final dessert, which can be cut or spooned into individual servings.
Solution 3:
Naming convention summary between British and American English.
+------------------+------------+------------+----------------------------------+------------------------------+
| American | British | French | Description | Contains fruit (or juice)? |
+------------------+------------+------------+----------------------------------+------------------------------+
| Jello | Jelly | Gelée | Gelatinous Dessert. | Gelée yes, others no |
| Jelly | Jam | Gelée | Smooth fruit spread. | Either fruit or fruit juice |
| Jam / Preserves | Jam | Confiture | Fruit spread containing pieces. | yes |
| Marmalade | Marmalade | Marmelade | Fruit spread containing peel. | mostly citrus |
+------------------+------------+------------+----------------------------------+------------------------------+
* In general, the smooth fruit spread is slightly gelatinous.
It seems like the confusion lies between the American 'Jelly' and the British 'Jam'. I have tried both and the one i tried didn't have real juice and was artificially flavored, but some do have fruit juice.
Gelée seems to fall into the categories of the American Jello/Jelly and confiture is more the traditional British Jam.