As said above the difference is due to camera to subject distance.
Largely the relative distance of parts of the subject. For example, a very close up headshot may have the subjects nose halfway between their ears and the camera. Being much closer it looks much larger. Great for artistic effect, not so flattering

As the camera gets closer the more the sides of the head fall out of view. If you get close enough the angle of view will only allow you to see the front of their face, the ears out of sight.
The same happens with full length shots. Stood next to someone, shooting from eye level, their head will be proportionally closer to the camera thus look larger and out of proportion with their legs.
Using a longer focal length forces you to step back putting parts of your subject a more equal, flattering, distance from the camera. Roughly speaking; 50mm (general,) -180mm (tight headshots,) is considered ideal.
As Terry said above, going longer shortens the apparent distances between points of your subject. Although not as dramatic as the 'wide angle' effect it is noticeable if you're looking for it.
This effect can also be used to make (groups of,) people look like they stood closer together.