In repetitively pulsed surface dielectric barrier discharge (SDBD), residual gas-phase species and dielectric surface charge generated by the preceding discharge evolve during the inter-pulse interval and can influence subsequent discharge development. To clarify the influence of the inter-pulse interval and the underlying mechanisms, a two-dimensional fluid model is used to simulate negative-polarity repetitive nanosecond-pulse SDBD. Three inter-pulse intervals (Δt = 10, 100, and 1000 ns) are considered under otherwise identical pulse conditions, and the evolution of the residual plasma channel, gas-phase species, and surface charge is analyzed together with the distribution of the reduced electric field. The results show that, as the inter-pulse interval increases, the pre-ionization level and spatial continuity of the residual plasma channel gradually decrease. Consequently, the subsequent discharge gradually changes from rapid development along the residual plasma channel and further propagation along the dielectric surface to localized re-initiation near the high-voltage electrode. This change is accompanied by radial contraction, local discontinuities, and a reduced propagation distance of the plasma channel, indicating a decreasing influence of the residual plasma channel on the subsequent discharge. The evolution of gas-phase species during the inter-pulse interval further shows that free electrons are rapidly depleted through attachment and electron-ion recombination, while the electron-impact ionization rate decreases rapidly as the reduced electric field decreases. At longer inter-pulse intervals, the dominant gas-phase species associated with the memory effect change from residual free electrons to negative ions and longlived reactive species. Electron detachment from O^- and O₂^- through reactions with O atoms contributes to electron production during the inter-pulse interval, but this process is insuffcient to maintain a high pre-ionization level in the residual plasma channel. In contrast, the dielectric surface charge has a longer relaxation timescale and can continue to influence the electric field distribution before the subsequent pulse is applied. These results indicate that both gas-phase and surface memory effects are involved in the influence of the preceding pulse on the subsequent discharge. As the inter-pulse interval increases, the contribution of gas-phase pre-ionization decreases relative to that of residual surface charge, while the subsequent discharge transitions from development along the residual plasma channel to localized re-initiation near the high-voltage electrode.