[lifthrasiir]

The original lossy WebP format is more or less an intra-coded frame format from VP8. This "I-frame-as-image" approach was considered good enough for some time, for example AVIF largely follows the same structure.

The WebP lossless format (internally "VP8L") is the second codec supported by libwebp but otherwise independent. This format can be thought as an optimized PNG; it uses the main PNG algorithm but then tweaks various bits for better compression. For this reason it is very rare to see PNG files smaller than losslessly compressed WebP files when efficiently done.

JPEG XL is very different from both. There are some technical resemblances, as the author of lossless WebP also worked on JPEG XL (and Brotli), but the overall architecture is completely revamped. The lossy portion of JPEG XL is a (much larger) superset of JPEG 1, while the lossless portion is based on a learnable context modelling respresented as a binary decision tree. And then everything got sandwiched between yet another set of components.

[JyrkiAlakuijala]

It would be more correct to say that PNG uses the GIF algorithm than that WebP uses the PNG algorithm.

WebP's select predictor and some other predictors are used in JPEG XL. The same for 2d locality map in backward references.

Both are able to use delta palettes. JPEG XL goes further by having a mixed mode where some entries are deltas for smooth gradients while others are usual palette entries.