A metaphorical model is one which is not dependent on a specific situation, nor a domain being modelled. Instead it is generic, giving transferable insight across a wide range of real-world situations. For example the models that describe limits to church growth are not calibrated for a particular congregation, and could be applied to growth barriers in other social organisations, businesses, populations or the environment. They are a metaphor for the types of processes that limit growth. Thus the models below have been "borrowed" from other domains.
As models become more fine-tuned to a given situation, they become less abstract, and more concrete, capable of being fine-tuned to data. As well as explaining particular observed behaviour and make more general predictions (Illustrative Models), they may give detailed forecasts of future behaviour and quantify possible interventions (Analogue Models). See Model Fidelity in John Morecroft, Strategic Modelling and Business Dynamics, 2007.
The metaphorical models below are constructed to illustrate the different barriers to growth, and how they may be tackled.