I had a 308 Norma Mag that was built on a 1903A3 action. It was a great cartridge.
As already mentioned, it is basically a 30-338WM. Norma invented the cartridge ,,, or copied the 30-338 in the late 1950s. At the time, you only had a choice of 300 HH, 300 weatherby or 308 Norma Mag.
About 3 or 4 years later, Winchester developed and marketed the 300 Winchester magnum which is very similar in size and performance.
Norma missed the marketing bandwagon by mis-naming the cartridge. Calling anything 308 at the time was just asking for trouble since the fairly new 308 Winchester (7.62 nato) was still being complained about by the old time hunters and rifleman.
If they would have called it the 300 Norma Magnum it would have sold much better and Winchester would have never had a reason to introduce a nearly identical cartridge.
The same with the wonderful 358 Norma Mag. If only they would have called it the 360 Alaskan or some darn thing... Instead, people confused it with the 358 Winchester.
You can make 308 Norma brass by resizing 338 Win Mag brass. Maybe even by messing with 300 Win Mag brass. Brass was a buck a round back when I sold mine.