Software defect prediction (SDP) is crucial for delivering high-quality software products. Recent research has indicated that prediction performance improvements in SDP are achievable by applying hyperparameter tuning to a particular SDP scenario. However, the positive impact resulting from the hyperparameter tuning step may differ based on the targeted SDP scenario. Comparing the impact of hyperparameter tuning across SDP scenarios is necessary to provide comprehensive insights and enhance the robustness, generalizability, and, eventually, the practicality of SDP modeling for quality assurance. Therefore, in this study, we contrast the impact of hyperparameter tuning across two pivotal and consecutive SDP scenarios: (1) Inner Version Defect Prediction (IVDP) and (2) Cross Version Defect Prediction (CVDP). The main distinctions between the two scenarios lie in the scope of defect prediction and the selected evaluation setups. This study's experiments use common evaluation setups, 28 machine learning (ML) algorithms, 53 post-release software datasets, two tuning algorithms, and five optimization metrics. We apply statistical analytics to compare the SDP performance impact differences by investigating the overall impact, the single ML algorithm impact, and variations across different software dataset sizes. The results indicate that the SDP gains within the IVDP scenario are significantly larger than those within the CVDP scenario. The results reveal that asserting performance gains for up to 24 out of 28 ML algorithms may not hold across multiple SDP scenarios. Furthermore, we found that small software datasets are more susceptible to larger differences in performance impacts. Overall, the study findings recommend software engineering researchers and practitioners to consider the effect of the selected SDP scenario when expecting performance gains from hyperparameter tuning.