On social media, the boundaries between people's private and public lives often blur. The need to navigate both roles, which are governed by distinct norms, impacts how individuals conduct themselves online, and presents methodological challenges for researchers. We conduct a systematic exploration on how an organization's official Twitter accounts and its members' personal accounts differ. Using a climate change Twitter data set as our case, we find substantial differences in activity and connectivity across the organizational levels we examined. The levels differed considerably in their overall retweet network structures, and accounts within each level were more likely to have similar connections than accounts at different levels. We illustrate the implications of these differences for applied research by showing that the levels closer to the core of the organization display more sectoral homophily but less triadic closure, and how each level consists of very different group structures. Our results show that the common practice of solely analyzing accounts from a single organizational level, grouping together all levels, or excluding certain levels can lead to a skewed understanding of how organizations are represented on social media.