This paper presents findings from a two-month comparative study involving a total of 36 participants using a social fitness application called HealthyTogether. Our aim was to understand whether and how patients with chronic diseases and healthy adults respond differently to social incentives, such as competition, cooperation, and accountability, and how these incentives could relate to their engagement in physical activities. We found that community leaderboard served different goals: healthy adults mainly used it to compete with others, and patients used it to validate their normalcy. For the patients, pairing up with strong ties fostered fulfilling fitness goals, while exercising with strangers diminished them. This study shows that social fitness application design for patients should take into account their need for support from communities and close relationships. Furthermore, our findings point towards opportunities for leveraging and modifying existing social fitness applications for patients' health management.