there are different types of modulus it depends on what types of stress is acting on the material if its direct stress then then there is modulus of elasticity,if tis shear stress then its modulus of rigidity and when its volumetric stress it is bulk modulus and so on

Yes, indeed.

Sometimes tensile modulus is different from flexural modulus, especially for composites.

But tensile modulus and elastic modulus and Young's modulus are equivalent terms.

The elastic modulus, also called Young's modulus, is identical to the tensile modulus. It relates stress to strain when loaded in tension.

The Young modulus and storage modulus measure two different things and use different formulas. A storage modulus measures the stored energy in a vibrating elastic material. The Young modulus measures the stress to in still elastic, and it is an elastic modulus.

Young's modulus