Sharpening algorithms might be statically defined rather than a bunch of weights, but they take a blurred image and create new data in it through approximations and heuristics defined in the algorithm.
I agree that it feels like there should be a difference, but I can't pin down what that actually is.
> create new data in it through approximations and heuristics defined in the algorithm
I guess the difference is where the algorithm gets it's input data from. Just sensor data or does it draw from a neural network that memorized a bunch of images / data store of images too.
You can argue what's the difference between this and Huawei replacing the image of the moon when their phone detects it with a hi-res one it has in storage - it's an "algorithm" too.
Are you using just the data provided to draw conclusions? Or do you include extra data from elsewhere to get your conclusions?
No. Every other technique is improving on raw data using that raw data and knowledge about ways to process data.
This is adding data, not just processing it.