Saturation plugins run the gamut from very subtle colouration all the way through what can essentially be used as guitar amp simulators. Fabfilter’s “Saturn/Saturn 2” is an example of a plugin that does all of those shades.
THD refers to “total harmonic distortion”, a figure which was often quoted in the days of hi-fi systems to boast about how little the particular hi-fi or hi-fi component had. It was considered an undesirable thing in that context.
However, in a modern digital context, modelling THD is often a desirable thing, because of the sense of “weight”, “warmth”, “realism”, “depth” or whatever other term you choose to use (insert applicable marketing term here to describe something sonically desirable).
Saturation is basically distortion. Generally speaking in audio land speak though, “saturation” as a term tends to be synonymous with the very subtle to subtle distortion imposed by traditional analogue circuitry and components like transformers and valves (tubes), and analogue tape.
Apart from the effects mentioned above, one of the most significant, desirable qualities of saturation (that I don’t think has been mentioned yet) is it’s ability to deal with sharp transient spikes in a digital context.
Because saturation absorbs transients so effectively, sounds like drums, percussion, acoustic guitars, pianos (basically anything that has a percussive, transient element) can be effectively made to sound “louder” and take up less headroom in the mix overall. It effectively “shaves off” the spiky transient with very little negative effect. As a result, the “body” of the sound can be turned up louder without reaching 0dB full scale, causing it to sound “fuller” and “louder” compared to the same sound without saturation, but with a much lower peak level.
The cumulative effect of using subtle saturation across many elements in a mix is that you end up with much more headroom overall. This means a mix that has been created using these methods has far greater overall “loudness potential” than one that hasn’t.
For example, if you manage to save 3dB of headroom across an entire mix by using this relatively benign and subtle method, your mix has the potential to be turned up an extra 3dB, which is a very noticeable difference. Save 10dB of headroom, turn up your mix 10dB and it will subjectively appear to be twice as loud.
This is one of the secrets as to why professional mixes appear to be so loud. Yes, they are mastered very loud, but the “loudness potential” is built into them from the start, so the mastering engineer doesn’t have to work as hard.
This is also the reason why many audio engineers struggled to move from the analogue realm to the digital early on. Many didn’t clearly understand (in a technical way) just how much all of these analogue components were saturating and softening transient material, both during the recording, mixing and mastering processes. They just perceived the results as “not as good”, so digital got a bad rap.
Thankfully, these days we have an abundance of processors that can model these effects and give us great results. It just comes down to understanding what they can do and making it work.