"$E$", "$K$", and "hardness", all indicate stiffness but are measured and used in different manners.
$E$ - Elastic modulus is defined as the slope of the tangent line to the stress-strain (elastic) curve. It is a material-specific quantity that measures the resistance to being deformed elastically when stress is applied to it, ...
Check out this link, it might help.
Should we use Hooke's Law (that linearly relates stresses to strains) if the stiffness of body is changing during deformation?
Now, the stiffness equation i.e. K = EA/L is only used for axial loading conditions. It is derived by dividing the load applied by max deflection. However, for bending cases, the bending stiffness ...
(Spring) Stiffness $K$ is a property of a structure which includes geometric and material effects.
On the other hand, Young's Modulus $E$ is a property of the material.
Bottom line is that given the same material (i.e. same Young's modulus), changing the cross-section A or the length L could result in different deformation.
for a given structure K is ...