When you swing or tilt the front, you take the lens off-axis, but it stays in the same place relative to the film, so no distortion.
If you swing or tilt the back, you move one edge of the film farther from the lens, making the image bigger, and the other edge of the film closer to the lens, making the image smaller. You're effectively using different focal lengths across the image area. This distortion is called "keystoning".
https://en.wikipedia.org/wiki/Keystone_effect
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