Understanding role of friction in block on block problems Consider two blocks stacked on top of one another. There is friction between the blocks but there is no friction between the lower block and the table. So the only frictional force that tends to retard the lower block is due to the friction between the blocks right? And the force that accelerates the body on top is only the frictional force?
Also, I fail to understand how there are different conditions for relative motion to occur between the blocks when the force is applied on the lower/upper block. 
 A: In this totally hypothetical situation, everything you said is correct. It's important to remember, however, that there must be a normal force between the bodies for the friction force to exist. In the most intuitive example, this force can be the reaction of the gravitational force (from Earth) from the upper body onto the lower one.
The only acceleration acting on the upper body is due to friction and the reaction to it is the only retarding force on the lower body.
As for the relative motion, in my understanding there are no different conditions depending on whether block the force is applied on. Of course, the block on which the force is being applied would move a larger distance (at a same time interval) than the other. 
I apologize for my terrible English.
A: If the force being applied is small, it can be applied to either block, and the static friction force will keep them accelerating together.  If it is large then the maximum static friction force will be exceeded, and the upper block will slide along the lower with constant kinetic friction force f = μN, where N is the weight of the upper block.  The block where the external force is applied will accelerate at: a = (F – f)/M,  and the other will accelerate at: a = f/m.
A: As long as the two blocks move together as one whole block, it does not matter you apply accelerating force to the upper or lower block.
But, if the accelerating force is greater than a threshold, the two bodies move in relative to each other, in this case, the threshold value and the resulting movement depend on which block you apply the force.
