S/N ratio has zero to do with distortion. It is how much noise (background hiss introduced by the amp) the amp introduces to the signal. It is expressed in dB and every 3 dB is a doubling of power. Once you get to a certain point, higher numbers are just that, higher numbers. The noise has gone below the level of audibility long ago and any increase beyond that is moot.
THD, total harmonic distortion, is the non linearity of an amp exhibited in multiples of the frequency tone fed to the amp, generally 1kHz for testing, expressed as a percentage of the output. Less than 1% is generally inaudible. Generally not included in THD is crossover distortion, a spike in the waveform not harmonic in nature caused by the output devices switching on and off, and it is quite audible. Many cheap amps have problems with this.