No. Shifting the lens and moving the camera body are not equivalent.

A shift lens moves the lens relative to the sensor, letting you choose a different part of the lens’s larger image circle while the camera itself stays in the same position. That changes framing without changing viewpoint or perspective.

Moving the whole camera changes the camera’s viewpoint relative to the subject. That changes perspective, even if the movement is small. The amount of visible change depends on subject distance: 5 mm of camera movement may be negligible for a distant subject, but lens shift is significant because it is large relative to sensor size.

So:

• Lens shift: reframes by sliding the projected image over the sensor.
• Camera movement: changes viewpoint relative to the scene.

This is why shift lenses are useful for architecture: you can keep the camera level and shift upward to include more of a building without introducing the perspective change you’d get by moving or tilting the camera. You can think of shift as selecting a different portion of a larger image circle, somewhat like cropping from a wider lens image, but using the full sensor area.