We present the largest study to date of star cluster mass and age distributions in nearby galaxies. The analysis is based on a uniformly selected catalog of over 15,000 (36,000) human- (machine-) classified compact clusters across 38 spiral galaxies in the PHANGS-Hubble Space Telescope survey, with improved photometric SED age dating that mitigates key degeneracies with reddening and metallicity. The galaxies span a factor of ~100 in star formation rate (SFR) and in their surface density of star formation and molecular gas (ΣSFR, ΣH2 ), and cover a broad range of morphologies. We find that cluster mass functions are well described by a power law, dN/dM ∝ Mβ, with β = -1.9 ± 0.2, and that this shape is remarkably similar across all galaxies in our sample and eight composite groups of galaxies with similar SFRs, with no significant dependence on SFR, ΣSFR, or ΣH2 . Cluster age distributions decline steeply and can be described by dN/dτ ∝ τγ with γ = -0.83 ± 0.24, again with little dependence on host-galaxy properties or cluster mass. The independence of the mass and age distributions implies a separable joint distribution, g(M, τ) ∝ Mβτγ, and suggests that cluster populations in spiral disks are dominated by strong, mass-independent dissolution over their first approximately gigayear. These results establish a benchmark for interpreting cluster demographics across diverse galactic environments and provide context for studies of young cluster populations at high redshift.