In almost all electroencephalography (EEG) recording setups, there are two auxiliary electrodes in addition to the ones used to record: the ground electrode and the reference electrode.
I've so far read two explanations for this. First, the explanation provided here is that the ground electrode is used for active grounding in a driven-right-leg (DRL) setup, so as to eliminate the common mode and thus increase the common mode rejection ratio (CMRR). Second, the explanation provided here is that to measure voltage, we need a signal ground, and that an electrophysiological signal only makes sense as the difference between two sites with non-zero value.
The first explanation does make sense to me, but the second one doesn't: can't you just measure everything as the difference between the site and the ground? The two seem quite contradictory...