I was struggling to understand what common mode voltage and CMRR is. I think eventually I understand what it is about. Before posing my new question I will briefly write about my drawing. On the left side in setup 1 varying v1 and v2 with respect to ground are applied as inputs of a differential amplifier. And at time "t" v1=5V and v2=1V. It means the amplifier will reject (5+1) / 2 = 3V common-mode voltage (at time t) and take the signals as +2V and -2V inputs (vd = 4V difference).
In setup 2 (kind of equivalent to setup 1) at time "t" v1'= +2V and v2'=-2V are applied as inputs of a differential amplifier. Similarly in this case vd = 4V potential difference between the inputs. But because in this case the common-mode voltage vcm=0 it looks like this measurement is more accurate because even it is non-ideal amplifier (having a common mode gain) it will not affect output voltage because vcm=0.
If I have a sensor like a strain gauge which setup is realistic in real life? In data acquisition systems when they use differential inputs instead of single inputs does that correspond to setup 2? Will v1 and v2 always at any time t be as such v1=-v2? I'm a bit confused relating to the real scenario.