I was always under the impression "Germany" i.e. the German Empire in Civ4 was a represent the northern chain of german empires, i.e. Prussia, and Modern Germany.
the HRE represented the southern german peoples, (Austria, Charlemagne's empire, Lombards, Burgundians, etc... leading up to the Austro-Hungarian Empire.
Just because the "peoples" were both from the german family of languages, doesn't necessarily mean their cultures are the same, (likewise with the Byzantines/Ancient Romans) I understand the Byzantines never called themselves that, and the name "Byzantine" was a label historians placed on the empire from the Split to the fall of Constantinople. The culture was different from Ancient Rome, this can be seen from the Architecture, Laws, Religion, Language (they spoke Greek), etc...