Is there a cause-effect relation in Newton's third law of motion?

This is because acceleration depends on both force and mass (F = ma).

We know that from Newton's Third Law. While action-reaction forces are always equal, the objects they act on usually have very different masses.

If you consider a falling stone and the Earth as an action-reaction pair. The Third Law tells us,  

• Earth pulls stone down with force F

• Stone pulls Earth up with equal force F

• But Earth's mass is enormous, so its acceleration is tiny (F/huge mass = tiny acceleration)

• Stone's mass is small, so its acceleration is large (F/small mass = large acceleration)

• Result: Stone falls noticeably, Earth's motion is unnoticeable.

Action-reaction forces act on different objects. That's why they don't or cannot cancel out.

For instance, when you push a wall, you can observe two things. 

• Your hand pushes the wall (action)

• The wall pushes your hand (reaction)

These are equal and opposite. But a close scientific examination will tell you that they are indeed acting on different things. To find your hand's motion, only consider the force on your hand (wall pushing back). The force from your hand affects the wall's motion, which is not yours.