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.
What is PNG?
PNG is the web's lossless image format: compression that never degrades the picture, and a real alpha channel for transparency. It is the right choice for screenshots, logos, line art and anything with sharp edges or text.