GIFs aren’t really designed for photos. The noise added is because of the conversion to 256 colours. And you’re right. It does often require more information be stored. The format is best for hand drawn images.
JPEG is a little different. It doesn’t store pixels directly. It stores 8×8 squares, made up of patterns [like these](https://upload.wikimedia.org/wikipedia/commons/2/24/DCT-8×8.png) added together. Generally real world images only need a few of them and the least important ones are removed to keep the image size down, but because most of them look like noise.
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