I noticed in my Tamiya Kommandeurwagen kit that the visor hat of the general figure looks no different from that of a lower-ranking officer. Are the visor hat types supposed to be identical or similar, or did the kit makers goof?

Until 1939 caps with leather visors were used by every german soldier- it was garrison cap- the only difference between officer's and private's cap was the belt over visor- officers wore silver cords, and the others- simple black leather belt. when war begun, garrison caps were only used by officers- soldiers wore various field caps.
the detail by which the caps of different ranks could be distinguished was colour of branch piping/ornamental cords, but not the cap visor.
Besides officers had often ther uniforms made by tailors- individual commisions paid by the army. there were many manufactures in germany that offered uniforms, caps, belts, insignia and so on.
so, thats why they differed from each other.