  In this work, we aim at providing a consistent analysis of the dust
properties from metal-poor to metal-rich environments by linking them to
fundamental galactic parameters. We consider two samples of galaxies: the Dwarf
Galaxy Survey (DGS) and KINGFISH, totalling 109 galaxies, spanning almost 2 dex
in metallicity. We collect infrared (IR) to submillimetre (submm) data for both
samples and present the complete data set for the DGS sample. We model the
observed spectral energy distributions (SED) with a physically-motivated dust
model to access the dust properties. Using a different SED model (modified
blackbody), dust composition (amorphous carbon), or wavelength coverage at
submm wavelengths results in differences in the dust mass estimate of a factor
two to three, showing that this parameter is subject to non-negligible
systematic modelling uncertainties. For eight galaxies in our sample, we find a
rather small excess at 500 microns (< 1.5 sigma). We find that the dust SED of
low-metallicity galaxies is broader and peaks at shorter wavelengths compared
to more metal-rich systems, a sign of a clumpier medium in dwarf galaxies. The
PAH mass fraction and the dust temperature distribution are found to be driven
mostly by the specific star-formation rate, SSFR, with secondary effects from
metallicity. The correlations between metallicity and dust mass or total-IR
luminosity are direct consequences of the stellar mass-metallicity relation.
The dust-to-stellar mass ratios of metal-rich sources follow the well-studied
trend of decreasing ratio for decreasing SSFR. The relation is more complex for
highly star-forming low-metallicity galaxies and depends on the chemical
evolutionary stage of the source (i.e., gas-to-dust mass ratio). Dust growth
processes in the ISM play a key role in the dust mass build-up with respect to
the stellar content at high SSFR and low metallicity. (abridged)
