Galactic nuclei typically host either a Nuclear Star Cluster (NSC, prevalent in galaxies with masses 10 10 M ) or a Massive Black Hole (MBH, common in galaxies with masses 10 12 M ). In the intermediate mass range, some nuclei host both a NSC and a MBH. In this paper, we explore scaling relations between NSC mass (M NSC ) and host galaxy total stellar mass (M ,gal ) using a large sample of NSCs in late-and earlytype 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 ∼ 1.5σ significant differences between NSCs in late-and early-type galaxies in the slopes and offsets of the relations r eff,NSC -M NSC , r eff,NSC -M ,gal and M NSC -M ,gal , in the sense that i) NSCs in late-types are more compact at fixed M NSC and M ,gal ; and ii) the M NSC -M ,gal relation is shallower for NSCs in late-types than in early-types, similar to the M BH -M ,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 eff,NSC . NSCs harbouring a sufficiently massive black hole are likely to exhibit surface brightness profile deviating from a typical King profile.