Aims. We perform a homogeneous analysis of an unprecedented set of spatially resolved scaling relations (SRs) between interstellar medium (ISM) components, that is to say dust, gas, and gas-phase metallicity, and other galaxy properties, such as stellar mass (M_star), total baryonic content, and star-formation rate (SFR), in a range of physical scales between 0.3 and 3.4 kpc. We also study some ratios between galaxy components: dust-to-stellar, dust-to-gas, and dust-to-metal ratios. Methods. We use a sample of 18 large, spiral, face-on DustPedia galaxies. The sample consists of galaxies with spatially resolved dust maps corresponding to 15 Herschel-SPIRE 500 μm resolution elements across the optical radius, with the morphological stage spanning from T = 2 to 8, M_star from 2 × 10⁹ to 1 × 10¹¹ M_⊙, SFR from 0.2 to 13 M_⊙ yr⁻¹, and oxygen abundance from 12 + log(O/H) = 8.3 to 8.8. Results. All the SRs are moderate or strong correlations except the dust-H I SR that does not exist or is weak for most galaxies. The SRs do not have a universal form but each galaxy is characterized by distinct correlations, affected by local processes and galaxy peculiarities. The SRs hold, on average, starting from the scale of 0.3 kpc, and if a breaking down scale exists it is below 0.3 kpc. By evaluating all galaxies together at the common scale of 3.4 kpc, differences due to peculiarities of individual galaxies are cancelled out and the corresponding SRs are consistent with those of whole galaxies. By comparing subgalactic and global scales, the most striking result emerges from the SRs involving ISM components: the dust-total gas SR is a good correlation at all scales, while the dust-H₂ and dust-H I SRs are good correlations at subkiloparsec/kiloparsec and total scales, respectively. For the other explored SRs, there is a good agreement between small and global scales and this may support the picture where the main physical processes regulating the properties and evolution of galaxies occur locally. In this scenario, our results are consistent with the hypothesis of self-regulation of the star-formation process. The analysis of subgalactic ratios between galaxy components shows that they are consistent with those derived for whole galaxies, from low to high redshift, supporting the idea that also these ratios could be set by local processes. Conclusions. Our results highlight the heterogeneity of galaxy properties and the importance of resolved studies on local galaxies in the context of galaxy evolution. They also provide fundamental observational constraints to theoretical models and updated references for high-redshift studies.