A GIF is a kind of picture that's often used on the internet. They can be animated, but the animated versions usually take up a lot of space. As pictures they're pretty small, but some detail is lost.
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A JPG is a kind of picture that's often used for photos. Pictures saved as JPEGs don't take up very much space, but their smaller size is because they're a little worse quality – most of the time small details will be lost.