What is HEIC?
HEIC is what an iPhone saves photos as, and it is not really an image format so much as a container holding HEVC video frames - the same codec used for film, applied to one still picture. It stores a photo at roughly half the size of the equivalent JPEG, which is why Apple switched to it, and it is also why so little else opens it: HEVC is patent-licensed, so most browsers and a good deal of desktop software cannot read a HEIC at all. Large photos are usually stored cut into tiles that have to be reassembled, not as one picture.
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.