Left circuit: One typical application is Vth+(N*vdsat) generation commonly used in cascade bias circuits. N in this expression can be programmed by adjusting top device size(this device will be in triode region). For simple cascode bias, we need Vth+2vdsat, for that 1/3 of the bottom device would be suffices.

Right circuit:  1. This is nothing but a diode connected transistor with less vds---if you bias the top device properly 2. Source follower with improved o/p impedance due to -ve feedback if you apply input at the top deice gate

Refer Gray and Mayer book, you will find excellent explanation of these.

Best Regards,
Raj.