This paper aims to situate Design by comparison to scientific modeling and optimal Decision. We introduce " generative functions " characterizing each of these activities. We formulate inputs, outputs and specific conditions of the generative functions corresponding to modeling (G m), Optimization (G o) and Design (G d): G d follows the classic view of modeling as a reduction of observed anomalies in knowledge by assuming the existence of unknown objects that may be observed and described with consistency and completeness. G o is possible when free parameters appear in models. Gd bears on recent Design theory, which shows that design begins with unknown yet not observable objects to which desired properties are assigned and have to be achieved by design. On this basis we establish that: i) modeling is a special case of Design; ii) the definition of design can be extended to the simultaneous generation of objects (as artifacts) and knowledge. Hence, the unity and variety of design can be explained, and we establish Design as a highly general generative function that is central to both science and decision. Such findings have several implications for research and education.