The pursuit of the progenitors of short duration-hard spectrum gamma-ray bursts (SHBs) draws strongly upon similar quests for the origin of supernovae (SNe) and long duration-soft spectrum GRBs (LSBs). Indeed the notion that, in the absence of smoking guns, the progenitors of cosmic explosions betray their identities both on the global and local scale, motivates the study of SHB redshifts, host galaxies, and locations with respect to hosts. To this end, we suggest both a historical and emergent physical analogy of GRBs with SNe: long-soft GRBs are to core-collapsed supernovae as short-hard GRBs are to Type Ia supernovae (``LSB:CC::SHB:Ia’'). Still, the SHB progenitor pursuit is just beginning and we caution that while there are some substantive differences between observations of LSBs and SHBs on large- scales, particularly in host demographics, neither the offset nor the redshift distributions of SHBs are yet (statistically) distinct with those of LSBs.