On the basis of a case study in bioengineering, this paper proposes a novel perspective on models in science and engineering. This is done with the help of two notions: representation and design. These two notions are interpreted as referring to modeling relations between vehicles and targets that differ in their respective directions of fit. The representation relation has a vehicle-to-target direction of fit and the design relation has a target-to-vehicle direction of fit. The case study of an organ on chip model illustrates that the technical device can participate in both design and representation relations. The two relations share the same relatum of the organ on chip, but they have different directions of fit. In the design relation, the chip is adjusted to a design plan, in which case we are dealing with a target-to-vehicle direction of fit. In the representation relation, the chip is adjusted to a human organ, in which case we are dealing with a vehicle-to-target direction of fit. The example shows that a conception of modeling as involving only relations with a vehicle-to-target direction of fit is too narrow to account for models in science and engineering.