The term "distortion" is used broadly to describe the result of audio passing through a non-linear process.
Some examples are clipping, analog tape saturation, "hard limiting" with very fast attack and release times, or distortion caused by transformers or tubes. Other examples of distortion in analog audio systems are harmonic and intermodulation distortion. Harmonic distortion (as the name implies) refers to the generation of harmonics of the input signal by the audio system. Intermodulation distortion is typically caused by an interference signal interacting with the input signal and is not harmonic in nature; making it much more audible at lower levels than harmonic distortion.
Non-linear processes in digital audio equipment can also cause distortion; and like intermodulation distortion, these distortions tend to be non-harmonic in nature and are more audible at lower levels than harmonic distortion as a result. On example of this type of distortion is the effect of jitter in clocking of conversion.