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GIF is big because it uses dictionary compression (pixel colors are mapped to a lookup table and then combinations of bits of increasing length are assigned to each table entry, the shortest combinations going for the most used colors, the longuest for the least used ones) which is great for stuff with clear (not-aliased) lines, a limited number of colors and large areas with just one flat color (such as drawings) but really bad for actual pictures (anything real world or imitating it, with natural shading).
I believe GIF still beats all or most other formats (except, for larger images, the actual vector graphics formats used in the programs with which such drawings are made nowadays) for things like drawings. (That said, I think PNG has a mode that does the same kind of compression, used for stuff like the little lemmy icon next to our nicknames here)
Animation on top if it was a bit of a hack due to the header format allowing multiple images in the same file, so it's really just a slideshow that has no video-oriented compression (i.e. each image is compressed individually and stored whole even if it's pretty much the last image with but a handful of pixels changed), hence why it's big when used for animation.
The kind of compression used in stuff like JPEG is based on the frequency of how each color channel changes across a block of pixels - which was 8x8 in the original JPEG - (i.e. it tries to match each block in the image to a sum of waves of different frequencies) which is much better for natural images, but loses information as a perfect match is usually impossible, and video compression methods have all sorts of intermediate frame compression techniques, the most basic of which is "this frame is the last frame with block such and such intact or moved around X pixels plus here's a bunch of entirelly new pixels" which usually is a lot better than compressing each image individually and storing it, not taking in account previous or subsequent images.
PS: I learned this stuff back at Uni, almost 3 decades ago, which shows you just how old this stuff is.