Both sides throw detail away. The left is a blur: every pixel becomes an average of its neighbors, so the texture goes, and the edges go with it. The right is a Kuwahara filter: the texture goes, but the edges stay sharp. That's why it looks painted instead of out of focus. Drag the line to compare.
Every pixel asks the same question: what does my neighborhood look like? Tap anywhere to see one pixel and the square of pixels around it, in their real colors. A blur would average all of them. Near an edge, that mixes two different things into mud.
The classic Kuwahara filter (1976) splits the neighborhood into four overlapping squares, one per corner. For each square it works out the average color and how much the colors vary, the spread. Then it keeps the average of the calmest square. Near an edge, one square usually sits entirely on one side, so its average belongs to that side and the edge survives.
The catch: squares in, squares out. Look closely at the picture and the brush marks are little rectangles.
This is the shader the site's cameras actually run, and the one Lightdab started from: a generalized Kuwahara filter (after Papari, with Kyprianidis's weights). The window is round and cut into eight overlapping slices with soft edges. Instead of one winner, it blends all eight averages, and calm slices count far more than busy ones. The edges stay, and the squares go.
Add a few flat bands of brightness and dark outlines from edge detection, and the photo turns into a cartoon. That's the Cel Shade Camera, and it's where Lightdab began.