The whole cross section is subjected to the same magnitude of tension in case of a tensile test. The scenario changes during bending test. The outer most layer is subjected to tension while the inner most layer is subjected to compression. Therefore, the strength will not be same in tensile test and bending test.
The tensile modulus (Young's modulus), or elastic modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials but whereas the flexural modulus or bending modulus is the ratio of stress to strain in flexural deformation, or the tendency for a material to bend.
A significant difference between the measurements made in bending and tension. The flexural strength is higher than the tensile one. Indeed, for two samples of the same size, only one-half of the sample is stressed in bending while the whole is in tension, then fewer defects are involved in bending.
However, if the same material was subjected to only tensile forces then all the fibers in the material are at the same stress and failure will initiate when the weakest fiber reaches its limiting tensile stress. Therefore, it is common for flexural strengths to be higher than tensile strengths for the same material.