What is GIF?

Thirty-five years old and still everywhere, because it does one thing nothing else quite does: animate inline, silently, in any context that displays an image. The cost is a 256-colour palette and no real motion compression, which makes GIF a poor way to store video and an excellent way to send a three-second loop.

What is ICO?

Windows icons, and a container rather than an image - one file holds the same icon at several sizes, so Windows can pick the right one for a title bar or a desktop. It tops out at 256x256 and supports transparency, which is what stops an icon looking like a sticker.