Several factors contribute to the traditional divide between translation and interpreting tasks. However, from the perspective of Cognitive Translation and Interpreting Studies (CTIS), it is a consequence of depicting them with a broad brush. While previously a convenient strategy to accommodate disciplinary approaches within Translation and Interpreting Studies, this approach is not optimal within CTIS. Once understood as monolithic modes, translation and interpreting increasingly appear to be variable clusters of features, and cognitive approaches need to take account of this new paradigm. The shared traits of these tasks can be reconsidered as multilectal mediated communication (MMC), including translation, localization, oral and signed interpreting, post-editing, transcreating, and transediting. This reconceptualization requires examining the foundations of theories about these tasks. This chapter explores modularity, memory, and mental lexicon as examples demonstrating the need to update referential frameworks and find common ground for MMC tasks within CTIS. Seeking higher granularity in the MMC tasks, and skeptical of the referential constructs and assumptions involved in data interpretation, the chapter includes a research review and suggests emerging trends.