Companding is a non-linear time-domain operation that alters the signal in way that reduces the influence of perceived noise. Small amplitude signal variations are increased above the noise floor so that when these are decreased on the receiving end the noise floor is lowered.
As any non-linear operation if transmitter and receiver are not exactly matched there will be harmonics and inter-modulation distortion introduced in the signal.
Companding was commonly used to reduce 12-bits of voice information in phone systems to 8 bits for transmission, and the noise this addressed is quantization noise. It mostly works due to the non-linear aspect of our auditory system. And due to the use of complementary non-linearities, it is better applied on the digital domain.
Pre-emphasis and equalization are linear frequency-domain operations that do not introduce harmonics or intermodulation distortion into the signal. These simply change the frequency response to compensate for the frequency response of the channel. Pre-emphasis, by placing more power on the most attenuated frequencies, attempts to place the signal above the noise floor on the receiver. Being a linear system, matching is not as critical.
Although pre-emphasis and equalization are common for data communication channels, the principle is related to what was used for Dolby B/C noise reduction technology for analog audio recordings (in this case a combination of pre-emphasis and automatic gain control (AGC) just for high frequencies was used to compress the dynamic range to remain above the noise floor. An AGC is a form of companding that, although still non-linear, avoids introducing harmonic distortion).
You would not normally use companding for analog music recordings, as the wide bandwidth and required complementary non-linearities would guarantee the introduction of harmonic distortion.
However, on some analog applications in which a wide dynamic range is required, there are filtering techniques that make use of analog companding. These are called log-domain filters.
A mixed technique that underlies all of our current lossy music formats from MP3 onward. Is the compansion of individual portions of the spectrum and the assignment of more or less bits (down to zero) to each portion of the signal spectrum. Our auditory system is highly non-linear and masks signals that lie too close to other larger signals that occur around the same time. These hearing models are used to compand the individual bands of the signal to save storage and transmission space.