Let me explain the 2 types of distortion before more confusion sets in.
Optical or lens distortion or geometric distortion (or just distortion) happens when striaght lines looks distorted due to the lens. Generally, the distortion can be classified and barrel or pincushion distortion. Some modern zoom lenses have more complex distortion that looks wavy like a bow. The distortion happens or is more pronounced nearer the edge of the photo. This distortion has nothing to do with the subject distance nor focal length and is purely due to the lens design, although cheaper wide angle lenses tends to give more barrel and cheaper telephoto lens tends to give more pincushion distortion. Compare Nikkor 16mm fisheye and 14mm rectilinear lens, the fisheye lens is design to have loads of barrel distortion while the 14mm lens is design to have minimal distortion.
The perspective distortion is due to the fact that objects nearer the lens looks larger than objects more distant. This distortion is more pronounced on a wide angle than a telephoto lens. This effect is also exagerated when nearer object is very close to the lens. This does not matter whether it is near the centre or the edge of the picture.
Therefore, care has to be taken with wide angle lens when perspective distortion can destroy the compostion, e.g. portraiture. Taking protraiture for example, although creativity may cause you to do otherwise, you generally want to keep the proportion of the human body. If you use a wide angle lens and put the head nearer to the lens than the rest of the body, the head is going to look out-of-proportionally larger than the body. Generally, telephoto lens will cause less of this problem. Many so-call portraiture lenses are medium telephoto lenses, 85mm, 105mm, 135mm, etc.