How hardness differ from stiffness?

In oversimplified terms, hardness is resistance to abrasion. Stiffness is resistance to bending.

Steel can be hard and stiff (like an i-beam) or hard and not stiff (like a spring). Wood can be stiff but not hard (like a 4x4 gate post).

Stiffness means inability (or great difficulty) to move something.

Hardness is very similar although it wouldn't necessary be stiff, more a hard feeling on the item (such as steel) which is hard but possibly not stiff.

Hardness - "Hardness describes how much energy it takes to deform (stretch, compress, bend, etc.) a material."

Stiffness - "Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force."

Stiffness is based on the relationship between stress and strain. Hardness is related to wear and can be changed as through heat treatments such as quench and tempering, or cold working. Please note that such treatments can alter the total amount of strain capacity especially in the plastic range.

Stiffness is the reciprocal of flexibility, a material can be flexible/stiff but not hard or it can be very hard.

Hardness has more to do with the surface resistance to deformation.

Hardness is response of inter-molecular structure of body against any force with zero displacement of the body.

Stiffness is response of inter-molecular structure of body against any force in repsect to degree of freedom and the temporary or permanent displacement of body or its faces.

Based on type of Hardness is measured as below:
Types of hardness measurements: scratch, indentation, and rebound
1. For Scratch Hardness: Mohs Hardness scale is from 1 to 10. As Diamond is hardest body we ever know is considered as 10.
2. For Indentation Hardness:Rockwell,Vickers,Shore, and Brinell scale
3. For Rebound Hardness:Leeb rebound hardness test and Bennett hardness scale.

Based on type of Stiffness is measured as below:
1.Stiffness is measured in one direction with respect to degree of Freedom in newtons per meter.
2.Rotational stiffness measured in newton-metres per radian because its angluar in direction.

Look up the definitions of each in Google!

https://en.wikipedia.org/wiki/Stiffness
https://en.wikipedia.org/wiki/Hardness

Hardness ---- it comes with its nature while the material was formed, and cannot be changed.
Stiffness ---- it happens from a softer state into a harder state, like the dead body turns from soft into stiffness after a few hours from dead. The state of stiffness can be altered back.