A design model is a model in which you specify the state of the working fluid along the cycle (its pressure, temperature, mass flow rate), as well as the energy transfers in the system, so as to characterize a design operating point. Assuming the components efficiencies, this kind of model permits to derive the geometries of the various components (like the heat exchangers surface area) so as to realize in practice the specified design conditions.
An off-design is the opposite. It is a model into wich you specify the geometries of the different components and the boundary conditions of the system, and it will compute the resulting state of the working fluid. The pressures/temperatures of the working fluid are not inputs of the model anymore, but they are outputs. This kind of model permits you to know how an exisiting machine, sized for a specified design point, will behave if you leave this design point.
I agree with Remi but for given geometry we measure fluid parameters like flow rate, pressure and temp. But how input fluid conditions are defined and how non linearity in fluid behavior is taken care of ??
I think off-design condition is some sort of condition which we use inputs which are not exactly the inputs that system has been designed to work on.
For example imagine we have designed an ORC unit which has been designed to work with 10 kg/m flow rate if we change this input we would be using this ORC unit in off-design condition
The clear differences between on-design and off-design in this context were masterfully established by the researcher Rémi Dickes , so I fully agree with his comment.