So, we can conclude hardness is focus on getting scar on the surface of material and strength is focus on an ability for resist the deformation from external force.

Differences between strength and hardness

Tensile or Compressive Stress, Strain, and Young’s Modulus

Tension or compression occurs when two antiparallel forces of equal magnitude act on an object along only one of its dimensions, in such a way that the object does not move. One way to envision such a situation is illustrated in Figure 1. A rod segment is either stretched or squeezed by a pair of forces acting along its length and perpendicular to its cross-section. The net effect of such forces is that the rod changes its length from the original length L0 that it had before the forces appeared, to a new length L that it has under the action of the forces. This change in length ΔL=L−L0 may be either elongation (when L is larger than the original length L0) or contraction (when L is smaller than the original length L0). Tensile stress and strain occur when the forces are stretching an object, causing its elongation, and the length change ΔL is positive. Compressive stress and strain occur when the forces are contracting an object, causing its shortening, and the length change ΔL is negative.

In either of these situations, we define stress as the ratio of the deforming force F⊥ to the cross-sectional area A of the object being deformed. The symbol F⊥ that we reserve for the deforming force means that this force acts perpendicularly to the cross-section of the object. Forces that act parallel to the cross-section do not change the length of an object. The definition of the tensile stress is

Tensile strain is the measure of the deformation of an object under tensile stress and is defined as the fractional change of the object’s length when the object experiences tensile stress Compressive stress and strain are defined by the same formulas, Equation 1 and Equation 2, respectively. The only difference from the tensile situation is that for compressive stress and strain, we take absolute values of the right-hand sides in Equation 1 and Equation 2 Figure 1 When an object is in either tension or compression, the net force on it is zero, but the object deforms by changing its original length L0. (a) Tension: The rod is elongated by ΔL. (b) Compression: The rod is contracted by ΔL. In both cases, the deforming force acts along the length of the rod and perpendicular to its cross-section. In the linear range of low stress, the cross-sectional area of the rod does not change.
Young’s modulus Y is the elastic modulus when deformation is caused by either tensile or compressive stress, and is defined by stress = (elastic modulus) × strain. Dividing this equation by tensile strain, we obtain the expression for Young’s modulus: Ref.

https://openstax.org/books/university-physics-volume-1/pages/12-3-stress-strain-and-elastic-modulus

https://www.makepartsfast.com/what-is-youngs-modulus-with-3d-printing-materials/

https://www.gemsociety.org/article/select-gems-ordered-mohs-hardness/

http://www.difference.minaprem.com/solid/difference-between-strength-and-hardness/