Enhancing is the correct term here, at least, in a technical context it is.
Image enhancement is defined as a process which aims to improve bad images so that they "look" better. Enhancement aims to make it look better to a human, and often but not always takes into account knowledge of the human visual system to get better looking results.
Image restoration is a defined as a process which aims to invert known degradation operations applied to image, such as pepper noise, scratches, or missing fragments of old photographs.
It's surprisingly to me how strongly you object to the word enhancement even though image processing textbooks are clear about the definition and have been using the word for decades. I think it shows some ignorance about how cameras and image processing works in modern devices.
It not be out of the ordinary for nobody to understand that what it is doing is impossible except for a few souls in the engineering department, who only agreed to implement it after repeated assurances from someone 8 steps removed from anything to do with communication, that the truth would be clearly communicated. I don't think anyone involved is lying, what happens in big corporations is that each of one hundred people distorts the truth by 1%, for a total distortion of 100%.
Of course there are details to be enhanced. The moon has craters. The craters are details. If a bad picture of the moon shows blurry craters, making the craters sharp enhances the details of the moon. I don't see where the lie is.
There could be a new crater by an asteroid that impacted the moon this morning. The crater is big, but not quite big enough to be visible on the blurred "real" image you shot this afternoon. After Samsung's alogrithm enhances the picture it has a level of detail in which the crater /should/ be visible, but since that enhancement is based on older images, the cater remains invisible.
This situation may seem contrived, but it is actually quite common that people disagree about details that were present at a certain event and try to resolve the disagreement by referring to photos. Now photos can nolonger be trusted as arbiters.
It doesn't even have to be a new crater. The moon wobbles throughout the month so that the part that faces the earth is slightly different through time. Combine with how close the moon is to the earth (which varies) and the amount that is lit up, each day's picture of the moon is fairly unique (at least unique enough over a largish data set).
I would hope that their enhancement software pulls the current timestamp and synthesizes a picture that would be the same as what would be taken from a real high resolution / telescopic image at that time and place.
One method uses the photo you actually took as the base and enhances from that. The other method used a random old picture of the moon from elsewhere and copypastes details of that onto your photos.
The distinction is significant, as for one of them your photo is the sole source of truth, while for the other it just "inserts" the image from elsewhere into your own photo. The former is expected, but the latter is not.
It's the same as the difference between enhancing a photo of yourself by doing some color/light processing or upscaling/sharpening using AI vs. "enhancing" by getting Brad Pitt's eyes and Angelina Jolie's nose copypasted onto a photo of your own face.
I'd argue that "enhancing details" is not the same as "replacing details".
Modifying the existing pixels captured by the sensor isn't the same as replacing an AI recognized section of the original pixels with other pixels entirely.
I think other interpretations of "enhance" aren't wrong either, since "enhance" is pretty subjective in the first place.
If there were suddenly a new crater on the moon whose photons were reaching the camera, and the AI algorithm decided that it didn't exist (and removed it) because older pictures of the moon didn't include it, I'd contest that the photo wasn't "enhanced."
