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Beginning with high- $T_c$cuprate materials, it has been observed that many superconductors exhibit so-called “Homes scaling,” in which the zero-temperature superfluid density ${\rho }_{s0}$is proportional to the product of the normal-state dc conductivity and the superconducting transition temperature ${\sigma }_{\mathrm{dc}}{T}_c$. For conventional, $s$-wave superconductors, such scaling has been shown to be a natural consequence of elastic-scattering disorder, not only in the extreme dirty limit, but across a broad range of scattering parameters. Here we show that when an analogous calculation is carried out for elastic scattering in $d$-wave superconductors, a stark contrast emerges, with ${\rho }_{s0}\propto {\left({\sigma }_{\mathrm{dc}}{T}_c\right)}^2$in the dirty limit, in apparent violation of Homes scaling. Within a simple approximate Migdal-Eliashberg treatment of inelastic scattering, we show how the observed Homes scaling is recovered. The normal-state behavior of near-optimally-doped cuprates is dominated by inelastic scattering, but significant deviations from Homes scaling occur for disorder-dominated cuprate systems, such as underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.333}$and overdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, and in very clean materials with little inelastic scattering, such as ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. We present a revised analysis where both axes of the original Homes scaling plot are normalized by the Drude plasma weight ${\omega }_{p,D}^2$and show that a new universal scaling emerges, in which the superfluid fractions of dirty $s$-wave and dirty $d$-wave superconductors coalesce to a single point at which normal-state scattering is occurring at the Planckian bound. The combined result is a new tool for classifying superconductors in terms of order parameter symmetry, as well as scattering strength and character. Although our model starts from a Fermi-liquid assumption, it describes underdoped cuprates surprisingly well.