The key difference between stress and strain is that stress is the internal resistance developed by the object to resist the deformation and strain is the ratio of change in dimension to the initial dimension of the object.
Before discussing the difference, let’s have a look at what stress and strain are.
Stress:
Stress can be defined as the ratio of internal resistance developed by the object to resist the deformation to the area of crosssection.
As shown in the below figure, the axial pressure applied tries to deform the object and the stress developed by the object helps to resist the deformation.
Mathematically, it can be expressed as,
Stress (σ) = `\mathbf{\frac{\text{Resisting force (F)}}{\text{Resisting area(A)}}}`
Stress is the tensor quantity and it is generally denoted by the symbol ‘σ (Sigma)’.
The stress can be classified as follows:
1] Longitudinal stress: The stress developed into the object to resist the change in length of the object is known as the longitudinal stress.
2] Shear stress: When the deformation is parallel to the direction of force and occurs by slipping of one plane over another then the stress developed is known as shear stress.
3] Volumetric stress: When the material deforms by changing its volume then the stress developed in a material is known as volumetric stress.
Strain:
Strain is the ratio of the change in the dimension to the original dimensions and it is denoted by the symbol ‘ε’.
Example:
The above figure shows the member of length ‘L’ subjected to the tensile load of ‘P’ which gets elongated by length ‘𝛿L’.
Thus the strain developed in the above member is given by,
ε = `\mathbf{\frac{\text{Change in length} (\deltaL)}{\text{Original length (L)}}}`
The strain can be classified into the following three types:
1] Longitudinal strain: If the application of load causes a change in length of the object then the strain obtained is known as longitudinal strain.
2] Shear strain: The strain caused in objects due to shear force is known as shear strain.
3] Volumetric strain: The ratio of change in volume of the object due to load to the original volume is known as volumetric strain.
Difference between stress and strain:
Sr. No.  Stress  Strain 

1]  Stress is the internal resistance developed by the object to avoid deformation.  Strain is the ratio of change in dimension to the initial dimension of the object. 
2]  Mathematically, it is given by, Stress = `\frac{\text{Resisting force (F)}}{\text{Resisting area(A)}}`  The strain can be calculated as, Strain = `\frac{\text{Final dimension – Original dimension}}{\text{Original dimension}}` 
3]  It is denoted by the symbol ‘σ’,  It is denoted by the symbol ‘ε’. 
4]  It is classified further as longitudinal stress, shear stress, volumetric stress.  It is classified as, longitudinal strain, shear strain, volumetric strain. 
5]  It has the SI unit of N/m².  It is a unitless quantity. 
6]  It has the dimensional formula of [M¹L⁻¹T⁻²].  It has no dimensional formula. 
7]  The stress cannot be measured directly and it is calculated by use of mathematical relations.  The strain can be measured directly by measuring the change in dimension. 
8]  The object can be stressed without causing strain.  The strain cannot occur without developing stress. 
FAQ’s:

What is the relation between stress & strain?
The relation between stress and strain is given by,
Stress / Strain = Elastic constant (E/G/K) 
How stress is different from the strain?
Stress is the resistance developed by the object to resist the deformation and strain is the change in dimension per initial dimensions of the object.
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