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 ICO?
ICO is the Windows icon container, and still what a browser fetches when it asks a site for /favicon.ico. One file can hold several sizes at once so the system can pick the right one; each dimension is stored in a single byte, which caps an icon at 256 pixels.