During software development, poor design and implementation choices can detrimentally impact software maintainability. Design smells, recurring patterns of poorly designed fragments, signify these issues. Role-stereotypes denote the generic responsibilities that classes assume in system design. Although the concepts of role-stereotypes and design smells differ, both significantly contribute to the design and maintenance of software systems. Understanding the relationship between these aspects is crucial for enhancing software maintainability, code quality, efficient code review, guided refactoring, and the design of role-specific metrics. This paper employs an exploratory approach, combining statistical analysis and unsupervised learning methods, to understand how design smells relate to role-stereotypes across desktop and mobile applications. Analyzing 11,350 classes from 30 GitHub repositories, we identified several design smells that frequently co-occur within certain role-stereotypes. Specifically, three (3) out of six (6) role-stereotypes we studied are more prone to design smells. We also examined the variation of design smells across the two ecosystems, driven by notable differences in their underlying architecture. Findings revealed that design smells are more prevalent in desktop than in mobile applications, especially within the Service Provider and Information Holder role-stereotypes. Additionally, the unsupervised learning method showed that certain pairs or groups of role-stereotypes are prone to similar types of design smells. We believe these relationships are associated with the characteristic and collaborative properties between role-stereotypes. The insights from this research provide valuable guidance for software teams on implementing design smell prevention and correction mechanisms, ensuring conceptual integrity during design and maintenance phases.