We introduce a new notion of isometry between immersions of a quad graph in Euclidean 3-space. In contrast to bar-joint frameworks, corresponding edges may not have the same length in 3-space. Instead, one compares using certain lifts to 4-space. This allows to capture the structure of smooth isometries, independent of resolution. Exemplifying this perspective, we discuss computational experiments immersing a 5x7 quadrangulation of a torus, which led to the discovery of analytic compact Bonnet pairs: two noncongruent tori that correspond via a mean-curvature preserving isometry (Bobenko, Hoffmann, S.-F., 2023). More generally, we develop spin (conformal) transformations, where an invariant spin cross-ratio generalizes the complex cross-ratio. This allows us to define non-planar quad nets in conformal coordinates, such as discrete Bonnet pairs. We also investigate one-parameter isometric associated families of discrete minimal surfaces. This is joint work with Tim Hoffmann and Max Wardetzky.