Plate action refers to the behavior of a plate when subjected to a force perpendicular to its surface, while skin action describes the behavior of a plate when the force acts in the plane of the plate. Plate action leads to bending stresses that vary across the cross section of the plate, while skin action generates membrane stresses that are uniform across the cross section. Skin action is more effective in utilizing the material strength compared to plate action and is often preferred for lightweight designs.