  There are known differences between the physical properties of HII and
diffuse ionized gas (DIG), but most of the studied regions in the literature
are relatively bright. We compiled a faint sample of 390 HII regions with
median $\log_{10}H\alpha$=34.7 in the spiral galaxy NGC300, derived their
physical properties in terms of metallicity, density, extinction, and
kinematics, and performed a comparative analysis of the properties of the DIG.
We used MUSE data of nine fields in NGC300, covering a galactocentric distance
of zero to ~450 arcsec (~4 projected kpc), including spiral arm and inter-arm
regions. We binned the data in dendrogram leaves and extracted all strong
nebular emission lines. We identified HII and DIG regions and compared their
electron densities, metallicity, extinction, and kinematic properties. We also
tested the effectiveness of unsupervised machine-learning algorithms in
distinguishing between the HII and DIG regions. The gas density in the HII and
DIG regions is close to the low-density limit in all fields. The average
velocity dispersion in the DIG is higher than in the HII regions, which can be
explained by the DIG being 1.8 kK hotter than HII gas. The DIG manifests a
lower ionization parameter than HII gas, and the DIG fractions vary between
15-77%, with strong evidence of a contribution by hot low-mass evolved stars
and shocks to the DIG ionization. Most of the DIG is consistent with no
extinction and an oxygen metallicity that is indistinguishable from that of the
HII gas.We observe a flat metallicity profile in the central region, without a
sign of a gradient. The differences between extremely faint HII and DIG regions
follow the same trends and correlations as their much brighter cousins. HII and
DIG are so heterogeneous, however, that the differences within each class are
larger than the differences between the two classes.
