Concreteness and abstraction are key in educational research in mathematics, both when discussing the nature of mathematics in itself, but also when exploring how to learn and teach mathematics. However, while the terms "concrete" and "abstract" are often used in the field, they are not always used with the same meaning. For example, the word "concrete" can be used to mean "specific," "relatable," "visual," and "tangible," while the word "abstract" can be used as "general," "rigorous," "vague," and "symbolic." While several scholars have emphasized the need for a multidimensional and fine-grained framework to articulate these differences in meaning, we further argue that it is crucial to precisely define how the terms "concrete" and "abstract" are actually used by the research community. Towards this goal, we offer three contributions. First, we empirically and systematically identify the various meanings of "concrete" and "abstract" used in the literature. Second, we offer a data-informed taxonomy to organize this semantic landscape and support research inquiry. And third, we offer templates for the design of future mathematics education interventions and studies.