Reform documents advocate for innovative pedagogical strategies to enhance student learning. A key innovation is the integration of science and engineering practices through engineering design (ED)-based physics laboratory tasks, where students tackle engineering design problems by applying physics principles. While this approach has its benefits, research shows that students do not always effectively apply scientific concepts, but instead rely on trial-and-error approaches, and end up "gadgeteering" their way to a solution. This leads to what is commonly referred to as the design-science gap--that students do not always consciously apply science concepts while solving a design problem. However, as obvious as the notion of a "gap" may appear, there seems to exist no consensus on the definitions of "design" and "science," further complicating the understanding of this gap. This qualitative study addresses the notion of the design-science gap by examining student groups' discussions and written lab reports from a multiweek ED-based undergraduate introductory physics laboratory task. Building on our earlier studies, we developed and employed a nuanced, multilayered coding scheme inspired by the Gioia Framework to characterize "design thinking" and "science thinking." We discuss how student groups engage in various aspects of design and how they apply physics concepts and principles to solve the problem. In the process, we demonstrate the interconnectedness of students' design thinking and science thinking. We advocate for the usage of the term "design-science connection" as opposed to "design-science gap" to deepen both design and science thinking. Our findings offer valuable insights for educators in design-based science education.