output resister of diode-connected MOSFET

Resistance can be defined as the ratio of the Change in Voltage (ΔV) to the Change in Current (ΔI).
So When a Change of Voltage of ΔV is applied at a terminal, a change is current of ΔI is measured and by taking the ratio, we get
R = ΔV/ΔI
If we consider the Transistor Equation, Id = Kn(W/L)(V_gs-V_th)²(1+λV_ds)
For a current source connected MOSFET (with Gate at fixed voltage), if we apply ΔV at the drain terminal, the only change in current is due to r_o of the transistor which is the λV_ds part.
But similarly, if we apply a change to both Gate and Drain which is the case in a Diode Connected Transistor, the change in the drain current is due to both the V_gs part (which gives the gm) as well as the V_ds part (which gives the r_o). Hence we get the (1/gm||r_o)
.
In other words, gm is the transconductance from Gate to Drain. And if we are measuring Drain Resistance with a fixed Gate voltage, gm will not matter since the Gate Voltage does not change.
But in case of a Diode Connected MOSFET, the Gate voltage also changes which in turn causes a change in the drain current if gm*v_gs

I hope I am making sense here...!