Leaving all the mathematics and boring word wizardry aside (photographers don't need to bother with technicalities, only with what looks good and with understanding how to get it), there is a fundamental difference between zooming and moving: perspective
When you zoom without moving (i.e. changing the distance between camera and subject), perspective remains the same. The only thing that changes is the "magnification".
|Zooming in without changing the camera-subject distance doesn't change the perspective. In all effect, zooming is simply a magnification|
You have probably seen an oft-used cinematography trick where the background seems to be "sucked in" - used often when the camera focuses on a character who just experienced something unexpected. Do you wanna know how it happens? The cinematographer changes the distance between camera and subject, using the zoom at the same time to keep the subject's size in the frame constant. As the perspective changes, the background seems to be moving.
Unfortunately, many beginners misunderstand the use of a zoom. Worse still, it teaches them bad habits. They become lazy, and the erroneous belief that a zoom is a substitute for their feet is fossilized. So, let me use my big bold font to emphasize this:
A zoom does NOT substitute your feet. Changing the focal length is NOT meant to be used when you want to go closer/farther.
|These kinds of shots are typical. Taken with a long tele, they compress perspective and help you achieve the desired effect.|
- Think of your desired perspective first. Do you want to emphasize the difference between foreground and background? Use a wide-angle. Do you want to compress the perspective, making objects that are physically further away to appear closer to your foreground? Use a long tele.
- If you are far away, move closer. If you are too close, take some steps back.
As simple as that, really.