What exactly is source reflection coefficient and input reflection coefficient?
what exactly are these two coefficient, 


The source reflection coefficient is the reflection coefficient of the source.

The input reflection coefficient is the reflection coefficient of the input port of the amplifier.


  why they are independent


They're independent because the source reflection coefficient is a property of the source, and the input reflection coefficient is a property of the amplifier.

They're independent because if you attached the source a different amplifier it would still have the same reflection coefficient. And if you attached the amplifier to a different source, it would still have the same input reflection coefficient.


  even the definition is kind of similar


The definitions are similar because the source is connected to the same wires as the amplifier input. So the source reflection and amplifier input reflection can both be expressed in terms of the travelling wave voltage on those wires.