Studies have suggested that there is a strong correlation between the masses of nuclear star clusters (NSCs) and their host galaxies, a correlation which is said to be an extension of the well-known correlations between supermassive black holes (SMBHs) and their host galaxies. But careful analysis of disk galaxies-including 2D bulge/disk/bar decompositions-shows that while SMBHs correlate with the stellar mass of the bulge component of galaxies, the masses of NSCs correlate much better with the total galaxy stellar mass. In addition, the mass ratio M-NSC/M-star,M- tot for NSCs in spirals (at least those with Hubble types Sc and later) is typically an order of magnitude smaller than the mass ratio M-BH/M-star,M- bul of SMBHs. The absence of a universal ``central massive object'' correlation argues against common formation and growth mechanisms for both SMBHs and NSCs. We also discuss evidence for a break in the NSC-host galaxy correlation, galaxies with Hubble types earlier than Sbc appear to host systematically more massive NSCs than do types Sc and later.