Conversational are a species of pragmatic implication1; they are implications of an act of 'saying'. The speaker's saying that p implies that q (given the presumption that he or she respects the norms of conversation --- Grice's 'maxims' --- or the overarching '
Geurts, B., & Pouscoulous, N. (2009). Embedded implicatures?!? Semantics and Pragmatics, 2. https://doi.org/10.3765/sp.2.4