What is the real purpose of analysing an amplifier with resistive or a current source load? How does its behaivor change?
The amplifier's performance - specifically gain - is a function of the load impedance, in different ways for each configuration, and is always a maximum into an infinite load impedance (i.e. a current source). Gain will be lower with a load resistance, depending on that load.

Seeing how each topology differs in this respect will let you understand practical circuits, and choose the best configuration for any purpose, such as to drive a specific load.