Situations are not forces.
But there are four forces in the scenario you described:
1). the force with which the person pushes the box
2). the normal force ... the wall pushes on the box in the opposite direction
3). gravity pulls the box downward
4). the force of static friction pushes the box upward.
#1 and #2 are balanced horizontal forces.
#3 and #4 are balanced vertical forces.
The net force on the box is zero.
So the box does not accelerate.
