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.

What is TGA?

Targa dates to 1984 and refuses to die, because game engines and 3D packages standardised on it for textures and never had a reason to move. It keeps an alpha channel, optionally compresses runs of identical pixels, and is simple enough that every tool reads it.