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There are known differences between the physical properties of HII anddiffuse ionized gas (DIG), but most of the studied regions in the literatureare relatively bright. We compiled a faint sample of 390 HII regions withmedian $\log_{10}H\alpha$=34.7 in the spiral galaxy NGC300, derived theirphysical properties in terms of metallicity, density, extinction, andkinematics, and performed a comparative analysis of the properties of the DIG.We used MUSE data of nine fields in NGC300, covering a galactocentric distanceof zero to ~450 arcsec (~4 projected kpc), including spiral arm and inter-armregions. We binned the data in dendrogram leaves and extracted all strongnebular emission lines. We identified HII and DIG regions and compared theirelectron densities, metallicity, extinction, and kinematic properties. We alsotested the effectiveness of unsupervised machine-learning algorithms indistinguishing between the HII and DIG regions. The gas density in the HII andDIG regions is close to the low-density limit in all fields. The averagevelocity dispersion in the DIG is higher than in the HII regions, which can beexplained by the DIG being 1.8 kK hotter than HII gas. The DIG manifests alower ionization parameter than HII gas, and the DIG fractions vary between15-77%, with strong evidence of a contribution by hot low-mass evolved starsand shocks to the DIG ionization. Most of the DIG is consistent with noextinction and an oxygen metallicity that is indistinguishable from that of theHII gas.We observe a flat metallicity profile in the central region, without asign of a gradient. The differences between extremely faint HII and DIG regionsfollow the same trends and correlations as their much brighter cousins. HII andDIG are so heterogeneous, however, that the differences within each class arelarger than the differences between the two classes.

MUSE crowded field 3D spectroscopy in NGC 300 III. Characterizing extremely faint HII regions and diffuse ionized gas