The best explanation of "Normal" as it applies to German cartridges is that in Dixon's "European Sporting Cartridges" vol I, page 126 under "Normalised Calibres". A few lines from that page illustrate the normalization concept:

"A major problem with the number of companies producing cartridges in Germany was that many introduced their own types similar but apparently non-interchangeable with other companies."

"Evidently beginning in 1909 the German arms industry (supported by DWM and RWS) established the official dimensions of a number of such calibres."

"Progressively through the 1920s, 30s, 40s and even into the 1950s, more calibres went through this process and were shown in DWM and RWS catalogs as being standardised."

Dixon then shows a table listing many cartridges and their "Normalised" dates, the 8x60S being before 1923 and the 8x60R before 1934. The plain 8x60 is not in that table, though it is suspicious that the 8x60S is in there twice. The earliest entries are dated 1912 and 1913 which include the 8x57 family (J, JR, JS, JRS) and the wildly variable 9,3x72R.

Basically a cartridge labeled as 'Normal' indicated that it adhered to the industry agreed upon standard dimensions. This means (to me anyway...) that a box of ammo labeled '8x60 Normal' would be built to standard cartridge dimensions and carry .318" bullets; I would also expect to find boxes of ammo out there that read '8x60S Normal' for those with 323" bullets as shown in m4220's post above.