MODULUS OF ELASTICITY: The ratio of stress to strain or the stiffness of the material of a structural member (resistance to deformation).
Essentially, the modulus of elasticity is a more general term regarding the overall stiffness of a member.
E= Modulus of Elasticity. If E increases, then so does the stiffness.
MOMENT OF INERTIA: The bending stiffness of a structural member’s cross-sectional shape.
Moment of inertia is specific to bending of the cross section of the member .
SECTION MODULUS: The ratio of the maximum moment on a beam and the maximum fiber stress (or moment of inertia over distance to nuetral axis of the member).
The section modulus is used to to find the minimum required beam that will support the bending load by looking in tables provided, such as in the Manual of Steel Construction.