In the commercial coated conductor tapes, the twinned structure of REBCO (REBa2Cu3O7-d, RE = Y and Gd) is characterized as either < 100 > or < 110 > orientation based on the tape length direction. In this study, we investigate the effects of the two different twinned structures on the critical current I-c of the REBCO tapes by combining; transport critical current and synchrotron radiation diffraction measurements. For the tapes with < 100 > oriented twins, we observed the inverted parabolic strain behavior on the uniaxial strain dependence of I-c. In contrast, the ones with < 110 > oriented twins showed a weak strain behavior without any maximum appeared in the strain dependence. Such a different uniaxial strain dependence was analyzed by using the one-dimensional twin model with different fractional lengths of A-domains and B-domains of REBCO twins. This model explains the essential features of the different uniaxial strain dependence we observed.