We find that the globular cluster (GC) systems of the Milky Way and of our neighboring spiral galaxy, M31, comprise two distinct entities, differing in three respects. First, M31 has a set of young GCs, ranging in age from a few times 102 Myr to 5 Gyr old, as well as old GCs. No such very young GCs are known in the Milky Way. Second, we confirm that the oldest M31 GCs have much higher nitrogen abundances than do Galactic GCs at equivalent metallicities, while carbon abundances appear normal for the GCs in both galaxies. Third, Morrison and coworkers have shown that M31 has a subcomponent of GCs that follow closely the disk rotation curve of that galaxy. Such a GC system in our own Galaxy has yet to be found. The only plausible scenario for the existence of the young M31 GC comes from the hierarchical-clustering-merging (HCM) paradigm for galaxy formation. We infer that M31 has absorbed more of its contingent of dwarf systems in the recent past than has the Milky Way. This inference has three implications: First, all spiral galaxies could differ in their GC properties, depending on how many companions each galaxy has and when the parent galaxy absorbs them. In this spectrum of possibilities, apparently the Milky Way ties down one end, in which almost all of its GCs were absorbed 10-12 Gyr ago. Second, it suggests that young GCs are preferentially formed in the dwarf companions of parent galaxies and then absorbed by the parent galaxy during mergers. Third, the young GCs seen in tidally interacting galaxies might come from the dwarf companions of these galaxies, rather than be made anew in the tidal interaction. However, there is no ready explanation for the marked difference in nitrogen abundance for the stars in the old M31 GCs relative to those in the oldest Galactic GCs, especially the most metal-poor GCs in both galaxies. The predictions made by Li & Burstein regarding the origin of nitrogen abundance in GCs are consistent with what is found for the old M31 GCs compared to that for the two 5 Gyr old M31 GCs. Observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.