  The properties of the stellar populations in a galaxy are known to correlate
with the amount and the distribution of stellar mass. We take advantage of the
maps of light-weighted mean stellar age Agewr and metallicity Z*wr for a sample
of 362 galaxies from the integral-field spectroscopic survey CALIFA (summing up
to >600,000 individual regions of approximately 1 kpc linear size), produced in
our previous works, to investigate how these local properties react to the
local stellar-mass surface density mu* and to the global total stellar mass M*
and mean stellar-mass surface density <mu>e. We establish the existence of i) a
dual mu*-Agewr relation, resulting in a young sequence and an old ridge, and
ii) a mu*-Z*wr relation, overall independent of the age of the regions. The
global mass parameters (M* and, possibly secondarily, <mu>e) determine the
distribution of mu* in a galaxy and set the maximum attainable mu*, which
increases with M*. M* affects the shape and normalization of the local
relations up to a threshold mass of $\sim 10^{10.3}$ MSun, above which they
remain unchanged. We conclude that stellar mass is a "glocal" (i.e.
simultaneously global and local) driver of the stellar population properties.
We consider how the local and global mass-age and mass-metallicity relations
are connected, and in particular discuss how it is possible, from a single
local relation, to produce two different global mass-metallicity relations for
quiescent and star-forming galaxies respectively, as reported in the
literature. Structural differences in these two classes of galaxies are key to
explain the duality in global scaling relations and appear as essential in
modelling the baryonic cycle of galaxies.
