Quantifying the degree of order and disorder in many-particle systems remains an outstanding problem in physics, materials science, and mathematics. To this end, we consider the translational order metric ${\tau }_T$, defined as the squared $L^2$ norm of the total correlation function $h\left(\mathbf{r}\right)$, and introduce its bond-orientational analog ${\tau }_O$, defined from the weighted total correlation function $h_{\mathbf{f}}\left(\mathbf{r}\right)$ using local orientational weights [S. Torquato et al., Phys. Rev. X 16, 011042 (2026)]. Unlike conventional metrics that quantify either positional order or spatially averaged orientational order, the pair $({\tau }_T,{\tau }_O)$ places both forms of order on a common two-point statistical footing, with each sensitive to the amplitude and spatial persistence of the corresponding correlation function. The translational order metric ${\tau }_T$ vanishes for a Poisson point process, whereas the geometry-derived weights yield a small, construction-dependent positive reference value of ${\tau }_O$; each metric diverges in systems possessing its corresponding form of long-range order. We compute both metrics for two nonhyperuniform sphere-packing models in two and three dimensions as functions of packing fraction $\varphi$: (1) equilibrium hard particles along the stable fluid branches up to near freezing and at selected values of $\varphi$ along the stable crystal branches, and (2) nonequilibrium random sequential addition (RSA) packings from the dilute regime to just below saturation. For the nonhyperuniform systems, bond-orientational order remains subdominant along the equilibrium-fluid and RSA configurations; however, its magnitude relative to the translational metric increases near the upper end of the equilibrium-fluid branches, much more strongly in two than in three dimensions, and the two metrics become comparable along the sampled crystal branches. At common packing fractions, equilibrium fluids and RSA packings trace distinct $({\tau }_T,{\tau }_O)$ trajectories, revealing preparation-dependent differences in structural order. As a representative hyperuniform family, we study 2D disordered stealthy hyperuniform (SHU) ground states for $0<\chi <1/2$, where $\chi$ is the stealthiness parameter. Within the disordered SHU phase, bond-orientational order remains subdominant, but its magnitude relative to the translational metric increases toward the disorder-to-order threshold. In all three models, ${\tau }_T$ and ${\tau }_O$ are positively correlated beyond the Poisson-reference regime: ${\tau }_O$ increases monotonically with ${\tau }_T$ across the sampled state points. These metrics may ultimately serve as collective structural coordinates for mapping freezing, melting, glass formation, jamming, self-assembly, and driven nonequilibrium transitions, as well as for enhanced sampling, phase classification, and inverse design.

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• Classical statistical mechanics