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 JPG?
JPEG is the format photographs live in. Its compression is lossy - it discards detail the eye is bad at noticing, and discards a little more every time the file is re-saved - which buys enormous size savings on photographic images and makes a mess of screenshots, logos and text. It has no transparency.