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There are a number of variables involved, including varying levels of compression. One big factor is screen size vs. image size. A picture displayed on a computer screen will often be resized to fit the screen. This might make it much smaller, but it can also make it larger. With the resolution of current screens, scaling may not be obvious. In addition, whether an image uses the entire screen or just a small part of the screen, a screenshot will, at least until it is edited, include the entire screen.

The flip side is that on a recent model phone you may have an 8 Megapixel (or more) camera but the phone display will be much lower resolution, so a screenshot on a phone is likely to take up much less space than the original image.