With the rapid development of the internet industry, online social networks have come to play an increasingly significant role in everyday life. In recent years, content-based emerging platforms such as TikTok, Instagram, and Bilibili have diverged fundamentally in their underlying logic from traditional connection-based social platforms like Facebook and LinkedIn. Empirical data on follower counts and follower-count-based rankings reveal that the distribution of social power varies significantly across different types of platforms, with content-based platforms exhibiting notably greater inequality. Here we propose two fundamental network formation mechanisms: a meritocracy-based model and a Matthew-effect-based model, designed to capture the formation logic underlying traditional and emerging social networks, respectively. Through theoretical and numerical analysis, we demonstrate that both models replicate salient statistical features of social networks including scale-free and small-world property, while also closely match empirical patterns on the relationship between in-degrees and in-degree rankings, thereby capturing the distinctive distributions of social power in respective platforms. Moreover, networks such as academic collaboration networks, where the distribution of social power usually lies between that of traditional and emerging platorms, can be interpreted through a hybrid of the two proposed mechanisms. Deconstructing the formation mechanisms of online social networks offers valuable insights into the evolution of the content ecosystems and the behavioral patterns of content creators on online social platforms.