The increasing surveillance by big tech companies or/and governments has raised concerns about the democratic and participatory structure of the datafied society. Meanwhile, over the course of the past decade, various bottom-up civic tech and digital civic initiatives have emerged to tackle pressing local issues, such as air pollution and disaster response, often via technology-mediated data collection, curation, analysis, design and visualisations, thus promoting democratic participation. In this article, we discuss how these data are understood in diverse contexts beyond the realm of civic tech and digital civics. In doing so, we explore the potential and limits of civic data by exploring the intersections of and differences between civic data and adjacent data-related concepts often used by civic tech communities themselves: counterdata and open data. Through our discursive exploration of these three data concepts, we conclude that understanding is limited when it comes to determining which data are ‘civic’, and that discussion of questions related to power structures, diversity and inclusion and infrastructuring of civic data has been minimal.