Metastability, disorder and jamming are the typical characteristics of amorphous systems, while the related structure changes remain unclear. Sphere packing is often used as a structure model for amorphous and crystalline states. In this article, sphere packing systems with packing densities ranging from 0.50 to 0.74 were simulated by using Discrete Element Method (DEM), and the obtained packing structures were assessed to investigate the densification process and jamming properties. An order parameter that can effectively distinguish the order and disorder of packing structures was proposed based on the distribution characteristics of jamming angles. Then the evolution of jamming characteristics during the transition from Random Loose Packing (RLP) to Random Close Packing (RCP) and the jamming-jamming relations of different packing structures were demonstrated. On this basis, a correlation between order-jamming-metastable states from the microscopic structural perspective was established, which is of valuable theoretical and practical implications for the characterization and synthesis of crystalline and amorphous materials.