What is GIF?
GIF is thirty-eight years old and refuses to die, because it animates and everything opens it. The cost is its palette: 256 colours per frame, so photographs come out visibly banded. Transparency is on-or-off per pixel, with no partial opacity.
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.