Moving screen vs boxing out

[Lotto]

Consider the two scenarios with the following question in mind: What in the rule book differentiates them? Why isn't the second one a moving screen according to the definitions given in Rule 4?

(1) A1 is dribbling, B1 defending. A2 sets a screen in B1's visual field. B1 moves with the intent to go around A2. A2 moves sideways into B1's path. Contact occurs with B1 hitting squarely into A1's torso.

Call: Moving screen, blocking foul on A1.

(2) A2 now is rebounding a shot. B1 is behind A2. B1 moves with the intent to go around A2. A2 moves sideways into B1's path. Contact occurs with B1 hitting squarely into A1's torso.

Call: Pushing foul on B1.