Difference between two gain +1 op-amp topologies
The upper opamp of circuit B works as a (positive) unity-gain amplifier - and R41 plays a special role !
In many cases, a unity gain configuration has a phase margin that is too small (step response with ringing effect or even instability). Here we have a circuit (unity gain) with a selectable loop gain which can be set to any value for ensuring a &quot;good&quot; and sufficient phase margin. Therefore, we even can use opamps which are not unity-gain- compensated.
In this circuit, the feedback factor is k=-R41/(R41+R40) and can be selected without touching the closed-loop gain of unity. More than that, both amplifier circuits (the upper and the lower one) can now have exactly the same loop gain for R40/R41=R43/R44 (same phase margin, same step response).
Without formal calculation we can see that the voltage Vp at the non-inv. input is Vp=Vin. For an ideal opamp with Vn=Vp=Vin there is no current through R41 and, hence, no current through R40. Therefore, wer have Vout=Vin and Vout/Vin=1.