Mobile health (mHealth) apps have gained recognition as effective means of delivering interventions for managing stress, offering accessible and scalable alternatives to traditional therapies. However, from a persuasion standpoint, there is a notable gap in the literature regarding the design and effectiveness of mobile-based behaviour change apps for stress management over the years. Therefore, we conduct a comparative analysis to explore trends in persuasive mobile apps for stress management (PMAS) in the literature and in the wild from 2003 to 2024 (21 years). Specifically, we identify the most frequently used persuasive strategies in PMAS design, including their operationalization and effectiveness. Additionally, we compare the persuasive strategies employed in the academic literature and those in commercial apps, as well as examine the therapeutic frameworks for intervention design, target audience, evaluation methods, and effectiveness of PMAS in reducing stress. Based on our findings, we developed a two-stage framework for designing effective PMAS and offer recommendations for future research to address identified gaps.