The concept of Wheatstones Bridge is used for the calculation of equivalent resistance only when there is a resistance in place of the galvanometer, i. e, when a restance is vertically connected; because in this case when the bridge is balanced, there is no current flowing through the resistance and therefore the presence or absence of this resistance does not affect anything. In this situation we remove the vertical resistance and then calculate the equivalent resistance.
But when a resistance is “horizontally” connected in the Wheatstones bridge, a current always flows through it irrespectictive of the fact that the bridge is balanced or not. therefore this resistance cannot be removed fot the calculation of equivalent reistance because its reoval will change the current in other branches of the circuit.