Does a push or pull always result in change of state of motion of an object? If no, why?

No, a push or pull does not always cause a change in motion because if there are opposing forces such as friction or an equal opposite force, the effect of the push or pull gets cancelled, like when we push against a wall and it does not move. Thus, whether motion changes or not depends on the strength of the applied force and the opposing forces acting on the object.