Melissa - casual research design is the same term for explanatory research design. Exploratory and explanatory designs would not usually be combined within a single methodological framework - as they are different processes with different outcomes. However, they could be used as two seperate data sets for multi-methods (same paradigm) or mixed methods (dual paradigm) approaches.
You might substitute ’causal’ with hypothetico-deductive (HD). How about ‘exploratory’? When the HD frame is unsuitable, we draw in case study. However, case study is bigger than ‘exploratory’. Cf.Article Parsing Competitive Dialogue in Public-Private Partnerships:...
I think that causal research usually means having a hypothesis, X causes Y, so that would not fit under the heading of exploratory research. Instead, exploratory research would ask questions like: What are the effects of X. Or, what causes Y?