  We use spatially resolved spectroscopy from the Calar Alto Legacy Field Area
(CALIFA) survey to study the nature of the line emitting gas in galaxies of
different Hubble types, focusing on the separation of star-forming (SF) regions
from those better characterized as diffuse ionized gas (DIG). The diagnosis is
carried out in terms of the equivalent width of ${\rm H}\alpha$ ($W_{{\rm
H}\alpha}$). Three nebular regimes are identified. Regions where $W_{{\rm
H}\alpha} < 3\ \AA$ define what we call the hDIG, the component of the DIG
where photoionization is dominated by hot, low-mass, evolved stars. Regions
where $W_{{\rm H}\alpha} > 14\ \AA$ trace SF complexes. $W_{{\rm H}\alpha}$
values in the intermediate 3--14 $\AA$ range reflect a mixed regime (mDIG)
where more than one process contributes. This three-tier scheme is inspired
both by theoretical and empirical considerations. Its application to CALIFA
galaxies of different types and inclinations leads to the following results:
$\textit{(i)}$ the hDIG component is prevalent throughout ellipticals and S0's
as well as in bulges, and explains the strongly bimodal distribution of
$W_{{\rm H}\alpha}$ both among and within galaxies. $\textit{(ii)}$ Early-type
spirals have some hDIG in their discs, but this component becomes progressively
less relevant for later Hubble types. $\textit{(iii)}$ hDIG emission is also
present above and below galactic discs, as seen in several edge-on spirals in
our sample. $\textit{(iv)}$ The SF/mDIG proportion grows steadily from early-
to late-type spirals, and from inner to outer radii. $\textit{(v)}$ Besides
circumventing basic inconsistencies in conventional DIG/SF separation criteria
based on the ${\rm H}\alpha$ surface brightness, our $W_{{\rm H}\alpha}$-based
method produces results in agreement with a classical excitation diagram
analysis.
