  In this paper we aim to (i) test the number of statistically distinct classes
required to classify the local galaxy population, and, (ii) identify the
differences in the physical and star formation properties of visually-distinct
galaxies. To accomplish this, we analyse the structural parameters (effective
radius r_e, effective surface brightness within r_e (mu_e), central surface
brightness (mu_0), and S'ersic index (n)), obtained by fitting the light
profile of 432 galaxies (0.002<z<=0.02 Viking Z-band), and their spectral
energy distribution using multi-band photometry in 18 broadbands to obtain the
stellar mass (M*), the star formation rate (SFR), the specific SFR (sSFR) and
the dust mass (M_{dust}), respectively.
  We show that visually distinct, star-forming dwarf galaxies (irregulars, blue
spheroids and low surface brightness galaxies) form a unimodal population in a
parameter space mapped by mu_e, mu_0, n, r_e, SFR, sSFR, M*, M_{dust} and
(g-i). The SFR and sSFR distribution of passively evolving (dwarf) ellipticals
on the other hand, statistically distinguish them from other galaxies with
similar luminosity, while the giant galaxies clearly segregate into
star-forming spirals and passive lenticulars. We therefore suggest that the
morphology classification scheme(s) used in literature for dwarf galaxies only
reflect the observational differences based on luminosity and surface
brightness among the apparent distinct classes, rather than any physical
differences between them.
