The structures of sodium aluminophosphate glasses prepared by both sol-gel as well as melt-cooling routes have been extensively characterized by high-resolution solid-state Na-23, Al-27, and P-31 single and double-resonance NMR techniques, including quantitative connectivity studies by Al-27 <-> P-31 and Na-23 <-> P-31 rotational echo double-resonance (REDOR) methods. Studies along four compositional lines, I: (AlPO4)(x)-(NaPO3)(1-x), II: (Na2O)(x)-(AlPO4)(1-x), III: (NaAlO2)(x)-(NaPO3)(1-x), and IV: (Al2O3)(x)(NaPO3)(1-x), reveal that the network structures of those glasses that are accessible by either preparation method are essentially identical. However, the significantly extended glass-forming ranges available by the sol-gel route facilitate exploration of the structure/composition relationships in more detail, revealing a number of interesting universal features throughout the whole glass system. Both short- and medium-range order appear to be controlled strongly by the O/P ratio of the glasses studied: Up to an O/P ratio of 3.5 (pyrophosphate composition), aluminum is predominantly six-coordinated and fully connected to phosphorus (Al(OP)(6) sites). In the region 3.5 <= O/P <= 4.0, a dramatic structural transformation takes place, leading to the appearance of additional four- and five-coordinated aluminum species whose second coordination spheres are also entirely dominated by phosphorus. The structure of glasses with an O/P ratio of precisely 4.0 (orthophosphate) is dominated by Al(OP)(4) units. As the O/P ratio increases beyond 4.0, the average extent of Al-O-P connectivity is decreased significantly. Here, new types of five- and six-coordinated aluminum units, which are only weakly connected to phosphorus, are formed, while the network modifier is attracted mainly by the phosphate units.