Structured sampling refers to the use of a combination of sampling and model-based methods. Instead of sampling the acoustic pressure wave, as in any typical audio recording, we sample more fundamental physical quantities such as an impulse response  that can be used to provide the desired level of both audio quality and model flexibility.
For example, in ``commuted waveguide synthesis'' (§8.7), the body resonator of a stringed instrument is efficiently modeled by its impulse response.
Another example is measuring the frequency response of a vibrating string so that a digital filter can be fit to that instead of being designed from first principles.
An advantage of sampling more fundamental characteristic signals such as impulse-responses is that they are often largely invariant with respect to controller state. This yields a far smaller memory footprint relative to brute force sampling of the acoustic pressure wave as a function of controller state.
There is an approximate continuum between sampling and physical modeling. That is, there is a wide range of possible hybrids between computational physical modeling and interpolation/manipulation of recorded samples. More computing power generally enables more accurate modeling and less memory usage.