In parallel to what Hawk wrote, AI image generation is similar. The idea is that through training you essentially produce an equation (really a bunch of weighted nodes, but functionally they boil down to a complicated equation) that can recognize a thing (say dogs), and can measure the likelihood any given image contains dogs.

If you run this equation backwards, it can take any image and show you how to make it look more like dogs. Do this for other categories of things. Now you ask for a dog lying in front of a doghouse chewing on a bone, it generates some white noise (think "snow" on an old TV) and ask the math to make it look maximally like a dog, doghouse, bone and chewing at the same time, possibly repeating a few times until the results don't get much more dog, doghouse, bone or chewing on another pass, and that's your generated image.

The reason they have trouble with things like hands is because we have pictures of all kinds of hands at all kinds of scales in all kinds of positions and the model doesn't have actual hands to compare to, just thousands upon thousands of pictures that say they contain hands to try figure out what a hand even is from statistical analysis of examples.

LLMs do something similar, but with words. They have a huge number of examples of writing, many of them tagged with descriptors, and are essentially piecing together an equation for what language looks like from statistical analysis of examples. The technique used for LLMs will never be anything more than a sufficiently advanced Chinese Room, not without serious alterations. That however doesn't mean it can't be useful.

For example, one could hypothetically amass a bunch of anonymized medical imaging including confirmed diagnoses and a bunch of healthy imaging and train a machine learning model to identify signs of disease and put priority flags and notes about detected potential diseases on the images to help expedite treatment when needed. After it's seen a few thousand times as many images as a real medical professional will see in their entire career it would even likely be more accurate than humans.