The physical motivation and interpretation of the stochastic propagation channel model of Saleh and Valenzuela are discussed in detail. This motivation mainly relies on assumptions on the stochastic properties of the positions of transmitter, receiver and scatterers in the propagation environment, and on the frequency range that is covered by the model. Some of these assumptions break down when the application of the model is extended from wideband to ultra-wideband propagation channels. Another important difference between these application contexts is the spatial scale over which the stochastic properties of the channel fluctuate when the transmitter or receiver is moved. This is further illustrated by analyzing the average power delay profile and some other channel properties for different levels of ensemble averaging, and discussing the relation between the ensemble averaging levels and the spatial variation scales. The notion of the averaging levels is essential for correct interpretation of the model, and hence for appropriate channel characterization and system design.