Much has been written about telecollaboration, though there is less research specifically on the precise affordances of computer-mediated communication (CMC) technologies used in telecollaborative projects. There are even fewer studies that investigate the affordances of CMC from the perspective of the community of inquiry (CoI) model, which posits that learning online occurs at the intersection of three types of presence, namely cognitive, social, and teaching. The goal of this paper is to examine data from a three-way intercultural online exchange between intact university classes in Germany, Poland, and the US, specifically analyzing the social and cognitive presences of the participants in two different types of discourse: synchronous video chats and asynchronous forum postings. The findings suggest that the synchronous video chats allow for comparable amounts of cognitive and social presence, while the asynchronous text forums are more conducive to cognitive presence as manifested in critical thinking, confirming that different digital tools have different affordances. However, the CoI model was found to be insufficient for explaining certain types of social presence, leading to adding to the subcategories of CoI coding, particularly as regards social presence in synchronous discourse.