  Galactic nuclei typically host either a Nuclear Star Cluster (NSC, prevalent
in galaxies with masses $\lesssim 10^{10}M_\odot$) or a Massive Black Hole
(MBH, common in galaxies with masses $\gtrsim 10^{12}M_\odot$). In the
intermediate mass range, some nuclei host both a NSC and a MBH. In this paper,
we explore scaling relations between NSC mass (${\cal M}_{\rm NSC}$) and host
galaxy total stellar mass (${\cal M}_{\star,\rm gal}$) using a large sample of
NSCs in late- and early-type galaxies, including a number of NSCs harboring a
MBH. Such scaling relations reflect the underlying physical mechanisms driving
the formation and (co)evolution of these central massive objects. We find
$\sim\!1.5\sigma$ significant differences between NSCs in late- and early-type
galaxies in the slopes and offsets of the relations $r_{\rm eff,NSC}$--${\cal
M}_{\rm NSC}$, $r_{\rm eff, NSC}$--${\cal M}_{\star,\rm gal}$ and ${\cal
M}_{\rm NSC}$--${\cal M}_{\star,\rm gal}$, in the sense that $i)$ NSCs in
late-types are more compact at fixed ${\cal M}_{\rm NSC}$ and ${\cal
M}_{\star,\rm gal}$; and $ii)$ the ${\cal M}_{\rm NSC}$--${\cal M}_{\star,\rm
gal}$ relation is shallower for NSCs in late-types than in early-types, similar
to the ${\cal M}_{\rm BH}$--${\cal M}_{\star,\rm bulge}$ relation. We discuss
these results in the context of the (possibly ongoing) evolution of NSCs,
depending on host galaxy type. For NSCs with a MBH, we illustrate the possible
influence of a MBH on its host NSC, by considering the ratio between the radius
of the MBH sphere of influence and $r_{\rm eff, NSC}$. NSCs harbouring a
sufficiently massive black hole are likely to exhibit surface brightness
profile deviating from a typical King profile.
