Presence, flow, narrative absorption, immersion, transportation, and similar subjective phenomena are studied in many different disciplines, mostly in relation to mediated experiences (books, film, VR, games). Moreover, since real, virtual, or fictional agents are often involved, concepts like identification and state empathy are often linked to engaging media use. Based on a scoping review which identified similarities in the wording of various questionnaire items conceived to measure different phenomena, we categorize items into the most relevant psychological aspects, and use this categorization to propose an interdisciplinary systematization. Then, based on a framework of embodied predictive processing, we present a new cognitive model of presence-related phenomena for mediated and non-mediated experiences, integrating spatial and temporal aspects and also considering the role of fiction and media design. Key processes described within the model are: selective attention, enactment of intentions, and interoception. We claim that presence is the state of perceived successful agency of an embodied mind able to correctly enact its predictions. The difference between real-life and simulated experiences (“book problem,” “paradox of fiction”) lays in the different precision weighing of exteroceptive and interoceptive signals.