The supply on the input terminals do not really 'exite' the bridge, but the strain on the sensors brings the bridge out of balance and can be measured on the output terminals. The supply is a passive voltage source.
But the question remains: is the Wheatstone bridge network exactly the same as...
(Quoting seems not to work...)
"The voltage across the bridge is reduced by the lead resistance, which reduces the excitation current."
Both are true, but not related as such. The higher overall resistance (Rb + 2*Rw) reduces Ie.
"The 4 resistor bridge looks like one resistor to the excitation...
Suppose a Wheatstone bridge with four equal active strain sensors (350 ohm each).
The output nodes are connected to a high impedance instrumentation amplifier, so no current draw from there. The bridge is placed at consiberable distance from the exitation voltage source (and the amplifier), so...