The internal structure of Jupiter is constrained by the precise gravity field measurements by NASA's Juno mission, atmospheric data from the Galileo entry probe, and Voyager radio occultations. Not only are these observations few compared to the possible interior setups and their multiple controlling parameters, but they remain challenging to reconcile. As a complex, multidimensional problem, characterizing typical structures can help simplify the modeling process. We used NeuralCMS, a deep learning model based on the accurate concentric Maclaurin spheroid (CMS) method, coupled with a fully consistent wind model to efficiently explore a wide range of interior models without prior assumptions. We then identified those consistent with the measurements and clustered the plausible combinations of parameters controlling the interior. We determine the plausible ranges of internal structures and the dynamical contributions to Jupiter's gravity field. Four typical interior structures are identified, characterized by their envelope and core properties. This reduces the dimensionality of Jupiter's interior to only two effective parameters. Within the reduced 2D phase space, we show that the most observationally constrained structures fall within one of the key structures, but they require a higher 1 bar temperature than the observed value. We provide a robust framework for characterizing giant planet interiors with consistent wind treatment, demonstrating that for Jupiter, wind constraints strongly impact the gravity harmonics while the interior parameter distribution remains largely unchanged. Importantly, we find that Jupiter's interior can be described by two effective parameters that clearly distinguish the four characteristic structures and conclude that atmospheric measurements may not fully represent the entire envelope.