It all boils down to what is called gain structure. You would like to make all pieces of equipment in your signal's chain to peak at the same time. This means they will peak for the same input signal altogether.
Assuming all pieces are linear (which is not the case but if you have favourite level regions for each piece of equipment you can set that as your target instead of the maximum) then, by making sure each piece peaks for the same signal it means that you have set your equipment in such a way that each and every piece uses all its available dynamic range, effectively setting the signal as far from the inherent noise of each machine as possible. This translates to maximising the Signal-to-Noise Ratio (SNR) of your setup.
Now, if you have already recorded the signal and try to apply digital gain, you most probably end up just bringing the recorded signal, along with all noise included higher in the digital dynamic range regime of your system. Most often than not, gain and level perform the same operation to the signal, multiplying, that is. The term may change from gain to level based on the stage this happens and from manufacturer to manufacturer. Nowadays, some good manufacturers may perform more complicated operations on the signal to avoid loss of numerical accuracy when attenuating signals but this has nothing to do with noise reduction.