Participation is a prevalent topic in many areas, and data-driven projects are no exception. While the term generally has positive connotations, ambiguities in participatory approaches between facilitators and participants are often noted. However, how facilitators can handle these ambiguities has been less studied. In this paper, we conduct a systematic literature review of participatory data-driven projects. We analyse 27 cases regarding their openness for participation and where participation most often occurs in the data life cycle. From our analysis, we describe three typical project structures of participatory data-driven projects, combining a focus on labour and resource participation and/or rule- and decision-making participation with the general set-up of the project as participatory-informed or participatory-at-core. From these combinations, different ambiguities arise. We discuss mitigations for these ambiguities through project policies and procedures for each type of project. Mitigating and clarifying ambiguities can support a more transparent and problem-oriented application of participatory processes in data-driven projects.