The stress sensitivity of shale caprock permeability is a critical factor influencing the long-term security of CO₂ geological sequestration systems. Substantial amounts of clay minerals and nanoscale pore structures reduce shale permeability by trapping water films and throat contraction. Conventional permeability models, which are based on homogeneous pore compressibility, tend to overestimate the contribution of non-effective pores to water mobility, resulting in significant inaccuracies in predicting stress-dependent permeability. Therefore, this study conducted NMR–seepage experiments under varying confining pressures on four shale samples with distinct lithologies to investigate pore compression deformation and permeability stress sensitivity. The T₂ cutoff was subsequently determined through displacement tests to distinguish seepage and adsorption pores. Two distinct constitutive models were calculated with respective compressibility coefficients. Finally, the effects of seepage and adsorption pores on shale permeability stress sensitivity were investigated. The results indicate the following. (1) Increasing confining pressure from 15 to 19 MPa reduces porosity by 14.2–39.6%, with permeability exhibiting a significant decline of 35.6–67.8%. (2) Adsorption pores, stabilized by bound water films of clay minerals, exhibit limited closure under stress. In contrast, seepage pores, influenced by brittle minerals, experience significant deformation, which predominantly contributes to permeability decline. (3) A dual-spring model, differentiating the compressibility of seepage and adsorption pores, reduces prediction errors by 92–96% compared to traditional models. These results highlight that neglecting pore-type-specific compressibility leads to overestimated permeability in heterogeneous shale, with critical implications for optimizing CO₂ storage integrity and hydrocarbon recovery strategies.