What is AVIF?
AVIF is a still image squeezed with the AV1 video codec, and it compresses harder than anything else in wide use - frequently half the size of a JPEG that looks the same. It handles transparency and high dynamic range. Support is good in browsers and patchy everywhere else, which is usually why people convert out of it.
What is WEBP?
WebP is Google's image format for the web, and the rare one that does both jobs: lossy compression that beats JPEG at the same quality, lossless compression that beats PNG, and an alpha channel either way. Every current browser reads it; older software often still does not.