This is a question that sounds basic, but I have yet to find an answer. When using a tilt-shift lens, if you shift the lens up 5 mm, or if you move the camera body up 5 mm, does the camera capture the same image?
When moving the camera body, the effect of the change is in relation to the subject. For example, when taking a photo of a person, 5 mm is quite unnoticeable. When shifting the lens, the effect of the shift is in relation to the imaging area size. In the case of full frame, a 5 mm shift up moves the whole image by 21 percent of the image height.
In principle, shifting a lens allows you to select which part of its image circle will land on the sensor. Therefore shift lenses have wider image circles than would be minimally needed for the sensor size from a non-shifting lens. So you can compare it to cropping from an image of a lens with a shorter focal length; the advantage of a shift lens is that you can use the sensor area and frame on spot.
The other answers by xenoid and Imre are perfectly correct, but for visual reference, I've created a graphic to display the difference. The blue cone is the camera in the original position, the red demonstrates raising the camera, and the green is a camera in the original position with only the lens raised to the same position.
Movement of the camera is relative to the subject, while movement of the lens is relative to the projected image, as Imre states. Usually the size of the image is much smaller than the subject, so lens movements can be much smaller than camera movements. That is why you might have to lift the camera in a crane to get the same framing as a tiny lens shift.
Here are some diagrams and photos to illustrate.
In the following diagram, the crossed lines represent the light rays. The green square represents the sensor. The shapes represent the physical object and image you wish to capture. In the normal position, the circle is captured on the sensor. A 40mm lens was used to take the photo.
Suppose you wish to capture the square. You could shift the lens up (or shift the sensor down). The sensor captures a different portion of the imaging circle, which contains the square. To take the photo, the 40mm lens was shifted upwards 1-2 cm.
If the imaging circle is too small, you will see its edge when you shift the lens. A 35mm lens was used to take this photo.
Suppose you want to move the camera up, with the sensor and lens in their normal alignment. The distance you'd have to move the camera is about the same as the distance between the circle and the square, which is much greater than the distance the sensor had to be shifted. The photo was taken after raising the camera about a foot. The aforementioned 40mm lens was used.
If you shift the camera up 5mm, you shift the captured image by 5 "absolute" millimeters. For instance, on a building, that would make the picture include or not the thickness of roof tiles.
If you shift the lens by 5mm on a 15mm-high sensor, you shift the capture image by one third of its relative size. If you shoot a building horizontally (to keep parallel verticals) the bottom half of your picture is the ground in front of the building. By shifting lens, you get one third of the ground and two thirds of building so you have more chances to include the full building.
See the diagram on Wikipedia.