hmmm good quetsion, and I see your confusion. The problem is that most examples aren't quite that simple. The space example is a good one. If I am floating in space, and I throw a ball in one direction, it will exert an equal force back on me and we will travel in opposite directions. The amount of force on each of us the same but we will accelerate a different rates because we have different masses. (force = mass * acceleration) since I am heavier than the ball (m is greater) my acceleration will be smaller.
Now think of some other examples, and then think of them in space! So on Earth, I push against a wall and the wall pushes back on me, the force I apply on the wall will not allow it to move significantly because of the mass of that wall (remember F=ma) and the friction holding the wall in place. Similarly, I have probably angled my feet to get optimum friction to stop me from moving back. Same situation in space, (thinking of a massive wall, i.e. a spaceship wall) I push on it and I am the one that flies off into space. There is no friction in this example so the only difference between us is our MASS. (F=ma again) as we both experience the same force, I accelerate more because I am smaller, the spaceship would appear not to move at all. So just because the forces are equal it does not mean nothing can move.
As for your car example it's a similar thing, the tyre exerts a force on the road and the road exerts a force on the tyre. The road is heavy, and held in place by all these other forces, so the only observable movement is by the car. If your wheels were stood on stacks of sheets of paper, the paper would fly out in the opposite direction, and the car would barely move. There is not enough friction to keep the paper where it is, and since the force on both the paper and the car is equal (but the car is so much heavier) then the paper would move but the car would not (well, barely).