I am a bit new to this field and I was reviewing some speech enhancement papers. These two terms keep popping up every once in a while so I was very confused as to what the difference between these two exactly is. I know that SNR is defined as logarithm of signal/noise, but I haven't come across SDR and haven't been able to understand the differences between these two.
In that case, you'll like another term, SINAD, Signal to Noise and Distortion.
Noise is unwanted signal correlated with no other signal. It's present whether the signal is there or not.
Distortion is unwanted signal correlated with the input signal. It's absent until the signal appears, and is usually not significant until the signal is occupying most of the dynamic range of the system.
I was aghast to learn recently that, when de-noising some recordings using Audacity, I discovered that 30dB was sufficiently good SNR during music passages that I couldn't tell the difference between that and perfect SNR. How my ears have aged!