For our test shots below, we used the same lens on both cameras- a Canon EF 50mm F1.8 II.
We also stood and center-focused on the exact same spots in both images.
We also stood and center-focused on the exact same spots in both images.
Image 2, above: shot with a Canon 40D (APS-C camera)
You can immediately notice a difference in the area that is covered in each shot. There was no zooming or edit cropping done to change the image area. These images are straight from the camera and what you would see through the viewfinder. So as mentioned before, the slightly wide angle of view with the lens changes to a slightly telephoto angle of view with the same lens, just with a switch in sensor size.
This is something to keep in mind when purchasing a non-digital designated lens to use on a digital SLR body that has the smaller APS-C size sensor. In this case (and using Canon as an example), the 50mm EF lens no longer acts as a true 50mm lens on the 40D. If you want to obtain a true 50mm and own one of the APS-C size digital SLRs, you would want to purchase a digital EF-S lens that is in the 50mm range, or an EF lens that is a smaller mm, or wider angle lens to start with.
This is something to keep in mind when purchasing a non-digital designated lens to use on a digital SLR body that has the smaller APS-C size sensor. In this case (and using Canon as an example), the 50mm EF lens no longer acts as a true 50mm lens on the 40D. If you want to obtain a true 50mm and own one of the APS-C size digital SLRs, you would want to purchase a digital EF-S lens that is in the 50mm range, or an EF lens that is a smaller mm, or wider angle lens to start with.

It would have been interesting if you had gone a little farther in discussing how (or if) going to a smaller mm lens to produce a similar size image would have other effects, such as a change of Depth of Field between say a 50mm lens and a 32mm lens.
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