In the literature, there are multiple definitions of integrated STEM education, resulting in ambiguity and uncertainty of application. A firm conception of integrated STEM education is needed to determine its content, procedures and epistemological knowledge, the latter being the focus of this article. While epistemological accounts exist for its several disciplines, an integrated STEM epistemology has not yet emerged. This article provides a comparative analysis of modeling and argumentation in mathematics, science, and engineering and notes the observed similarities, intersections, and differences of their practice in these fields. Emphasis is given to the differences, which have not been elaborated in current literature although their importance has been noted. In this context, we examine definitions and functions of models and arguments in science and mathematics. The difference in argumentation concerns mainly the validation of knowledge; in models, the differences pertain to their constitution and intended aim. We also describe mathematical modeling, which optimally illustrates the interplay and collaboration of mathematics and science and permits comparison of their respective practices. The article contributes to the issue of the interrelated diversity of STEM practices and the intellectual and pragmatic educational benefits this issue confers.