Some examples to show different types of distortions associated with wide angle lenses before everyone spiral further into the realm of confusion.
This photo shows perspective distortions. Notice the desk and floor tiles on the left and foreground were being stretched and deformed? This is the same kind of distortion which causes faces to stretch if you place your human subjects too close to the edges of the frame. These distortions cannot be corrected but can be minimised depending on how you frame the intended subjects e.g. not having your subjects placed too close to the edges of the frame. Such distortions can also be used to create dramatic and dynamic compositions if used properly.
This photo shows curvilinear distortions (barrel distortions) to be exact, which is associated with wide angle lenses. Notice the straight lines at the edges of the frame started bowing outwards? This is the type of distortion which can be corrected but there is usually a limit of what you can correct also. Same with perspective distortions, curvilinear distortions can be avoided if you place your lines further away from the edges.