This position paper is motivated by recent educational reform efforts that urge the integration of engineering in science education. We argue that it is plausible and beneficial to integrate engineering into formal K-12 science education. We illustrate how current literature, though often implicitly, discusses this integration from a pedagogical, epistemological, or methodological argumentative stance. From a pedagogical perspective, a historically dominant argument emphasizes how engineering helps make abstract science concepts more concrete. The epistemological argument is centered on how engineering is inherently interdisciplinary and hence its integrative role in support of scientific literacy and more broadly STEM literacy is natural. From a methodological perspective, arguments focus on the engineering design process, which is compatible with scientific inquiry and adaptable to answering different types of engineering questions. We call for the necessity of spelling out these arguments and call for common language as science and engineering educators form a research-base on the integration of science and engineering. We specifically provide and discuss specific terminology associated with four different models, each effectively used to integrate engineering into school science. We caution educators against a possible direction towards a convergence approach for a specific type of integrating engineering and science. Diversity in teaching models, more accurately represents the nature of engineering but also allows adaptations based on available school resources. Future synthesis can then examine student learning outcomes associated with different teaching models.