Is stiffness and modulus the same?

Hint: Firstly we need to understand what is meant by stiffness. The stiffness of an element can be referred to as how it bends under any load while maintaining its initial shape after the stress is removed. Stiffness is connected to elastic deformation due to the fact that the element's dimensions will not change after we remove the load. It is possible to have both good strength and low stiffness of the material.

Complete step by step solution:
The Young's modulus which is represented as (E) is the property of the material that determines how we can easily stretch and deformed and is also defined as the ratio of tensile stress which is represented as (\[\sigma \]) to the tensile strain which is represented as (\[\varepsilon \]). Where stress can be determined as the amount of force applied per unit area and also strain is the extension per unit length.

Stiffness has described the extent to which an object bends or we can say that object resists deformation and it returns to its original shape when we remove applied force.
The formula for stiffness $F=Kx$.............(where K is constant)
Formula for elastic modulus, \[E = \dfrac{{Stress}}{{Strain}}\]

Elastic modulus is also known as young’s modulus. Stiffness and young’s modulus both are proportional to each other. That means if the young modulus is high then the elastic deformation is small or we can say that the elastic modulus can measure the stiffness of the material.

Hence stiffness and modulus are proportional to each other.

Note: If a material contains stiffness, it must be strong enough to support a notable weight. Material can be both strong as well as elastic or it can be both strong and rigid but on the hand, we say that both are different properties.