Diode-connected PMOS
The relation you have asked for in the question is wrong. 

In the diode connected PMOS, fig.B, Gate and Drain are shorted. 
Hence \$V_G = V_D\$. 

And therefore \$V_{GD} = 0 \$ and \$V_{GS} = V_{DS}\$. 

M2 will always be in saturation as \$ V_{DS} &gt; V_{GS} - V_{Th} \$ always.