Was there any official distinction between the IBM 6580 Displaywriter System's beam spring and Model F keyboard variants?

Yes! The beam spring keyboard is known as Type A and the Model F keyboard is known as Type B. The February 1983 revision of the IBM Displaywriter System Product Support Manual describes these terms on Chapter 5 (Keyboard), specifically on page 64 of the bitsavers' PDF scan of this document. Figures showing the Type A and Type B assemblies are visible on page 63 (Figure 5-1) and page 64 (Figure 5-2) respectively.