I think that the definition of 'Germany' applied to the Middle-Ages is quite vague, as the modern concept of German nation was developed during the 18th-19th centuries.
The HRE refered to 'the German nation' because the speakers of West Germanic dialects became prominent inside the Empire and the Roman/Latin one became secondary, and the Reformation increased the cultural/social split between the different cultural components.
But during the early stages of the post-Verdun HRE, the concept of 'German nation' would not be applied, while 'Germany' as territory refered to the Roman Germania. The ideal of the Empire was often depicted in art with the feminized figures of (Roman) Germania, Italia, Gallia and Slavia making offers to the Emperor, and the religious (Western Christian) component clearly overlapped the ethnic/cultural ones (in fact, one of the reasons why the HRE did not care much about southern Italy it was because it was considered 'Eastern Christian' until 11th-12th centuries).